The first known keratoscope target was the image of a window, as reported by Scheiner in 1619 using natural light. He estimated the corneal curvature by comparing the window pane corneal reflection to those of a series of marbles until he found one that gave an image the same size as that of the cornea.¹ In 1820 Cuignet developed a keratoscope through which he observed the reflected image of an illuminated target held in front of a patient's cornea. His major problem was in the alignment of the light, target, and observer with the patient's visual axis. This was overcome in 1882 by Placido, who placed an observation hole in the center of the target.² Placido's target of alternating black and white rings (the Placido disk) has been embodied in many devices that are currently used to measure corneal topography, hence the term Placido disk keratoscopy.

A modern version of the original Placido disk is the Klein hand-held keratoscope (Fig. 1). This device is useful for detecting the location of tight sutures, irregular astigmatism, and keratoconus, all of which can be detected by mire pattern recognition. Its main limitations are that its mire pattern has an outer diameter of 5.5 mm, limiting its utility for evaluating peripheral topography. In addition there is no mechanism to achieve alignment other than user estimation, which introduces significant error in subjective interpretation.¹ Photokeratoscopes (e.g., Corneascope: Keravision, Santa Clara, CA) project a series of concentric circular mires that form a virtual image located within the anterior chamber of the eye. Information regarding the power of the anterior corneal surfaces is derived from visual inspection of the size and shape of the mires.

Simultaneously, information regarding the radius of curvature of a localized area of the cornea can be obtained by observing the separation between the mires reflected from that area of the cornea. In areas of steep cornea, the images of the mires are smaller, so the rings appear narrower and closer together. In the presence of regular astigmatism, the mires appear elliptic, the short axis of the ellipse corresponding to the meridian corneal steepening and highest power.³ Irregular astigmatism produces nonelliptic distortion of the mires. For the most part, photokeratoscopes yield qualitative information that is clinically useful as a means of evaluating changes in the peripheral cornea, such as in the detection of the corneal ectasia associated with keratoconus (Fig. 2), or as a guide to selective suture removal after penetrating keratoplasty. Its limitations are that it provides no information about the central 3 mm of the cornea and that up to 3 diopters of cylinder may go undetected by visual inspection of photokeratographs.

Quantitative analysis of photokeratograms became practical when Gullstrand in 1896 applied photography to keratoscopy (photokeratoscopy).³ This allowed the clinician to fix the image and measure the size of the rings; however, this analysis is slow and subject to major errors.³ In the 1980s, computer power was adapted to the task of automated high-resolution corneal topography analysis, which is most popularly implemented in commercially available computer-assisted videokeratoscopes, such as the Topographic Modeling System (TMS-1) (Computed Anatomy, New York, NY) and the Corneal Analysis System (Eysys Laboratories, Houston, TX). These devices were devised in order to overcome the deficiencies of photokeratoscopes both in speed and in gathering quantitative information about the anterior corneal surface.⁴ Most systems use illuminated Placido-type mires with nosecones that provide a broad area of corneal coverage from the apex to the limbus of the cornea, covering approximately 11 mm of cornea (Fig. 3). These novel conical mire targets provide very high radial resolution, being approximately 0.17 mm apart reflected on the normal corneal surface. Additionally, the central fixation light and the first mire of the standard cone provide excellent central corneal coverage, ensuring that corneal topographic details important to visual function are not obscured as they are with keratometers and traditional keratoscopic targets. Because direct measurements are made from the centrally visually important area as well as from the periphery, a clinically complete data set derived from between 6000 and 11,000 data points on the cornea is available for clinical interpretation. Other advantages of videokeratoscopy over photokeratoscopy are its speed in gathering quantitative information and its ability to display data in a clinically useful format with reasonable accuracy.^5–7

When the three targets overlap, maximum focus has been reached and an electronic snapshot of the video picture of the reflection of the Placido mires is taken. The computer analyzes the image to determine the size and shape of the mires; it reconstructs the patient's corneal surface and presents a graphic picture of the patient's topography in a suitable form.

The most useful form of data presentation is a color-coded corneal contour map in which steep areas are depicted as “hot colors,” such as reds and browns, and shallow areas as “cool colors,” such as blues and greens (Fig. 6). Two scales are commonly used: absolute and normalized. In the absolute scale, each color represents a 1.5-diopter interval between 35 and 50 diopters, whereas above and below this range, colors represent 5-diopter intervals. This scale is useful in routine practice (e.g., preoperative screening). In the normalized scale, the cornea is divided into 11 equal colors spanning that eye's total dioptric power. In this scale, more minute topographic details within an individual cornea are appreciated.^8,9 An isometric plot is also available in which the cornea is viewed side on, allowing the observer to appreciate the relative depth of a corneal incision. As part of the topographic display, quantitative indices are also generated, including the following: predicted visual acuity based on corneal shape, simulated keratometry readings, minimum keratometry reading, surface regularity index, and surface asymmetry index.¹⁰

CALCULATION OF CORNEAL SURFACE POWER

Videokeratoscopic analysis of corneal shape relies on the optical principal that the tear film on the anterior corneal surface acts as a convex mirror. A light (mire) shined toward the cornea gives rise to a virtually erect image located approximately 4 mm posterior to the anterior surface of the cornea, at the level of the anterior lens capsule. This is the corneal light reflex, or first Purkinje-Sanson's image, which is viewed during both keratoscopy and keratometry. The size of this image can be used to quantify the curvature of the cornea: the steeper the cornea (i.e., the smaller the radius of curvature), the more powerful the convex mirror it is, and the smaller the image will be. By the same principles, any toricity (different radii of curvature in different meridians) or irregularity of the corneal surface will cause a regular or irregular distortion of the image.² The image formed by a convex mirror can be constructed using two rays: (1) a ray parallel to the principal axis, which is reflected away from the principal focus; and (2) a ray from the top of the object traveling toward the center of curvature and reflecting back along the same path (Fig. 7). The magnification produced by a curved mirror is the ratio of the image size (I) to the object size (O); this, in turn, is proportional to the ratio of the distances of the image (v) and the object (u) from the mirror, as follows:

Magnification = I/O = v/u

In practice, the image (I) is located very close to the focal point (F), which is halfway between the center of curvature of the mirror (C, at the principal focus) and the mirror itself. Therefore v may be taken to equal half the radius of curvature of the mirror (r/2). Upon substituting r/2 for v in the preceding equation (I = O × r/2u) it can be seen that as the cornea becomes steeper and its radius of curvature (r) becomes smaller, so the image (I) also becomes smaller, and the topography mires appear closer together.

In a given keratometer, u is constant, being the focal distance of the viewing telescope. Rearrangement of the equation (r = 2u × I/O) shows that the radius of curvature is proportional to the image size if the object size remains constant.² The geometric optics equation that relates corneal power in diopters (D) to the radius of corneal curvature (R_c, measured in millimeters) is adapted from Snell's Law of Refraction, with differences of refractive index combined with corneal thickness and corneal back surface power to give the following equation:

D = K_i/R_c

where K_i is the keratometric index usually assigned a numeric value of 337.5. For example, a cornea with a radius of curvature (R_c) of 7.8 mm equates with this convention to a corneal power of 43.25 diopters (i.e., 337.5/7.8). The keratometric index differs from the corneal refractive index (1.376) in that it takes into account both the anterior and posterior corneal surfaces; however, it fails to recognize the differing refractive properties of the epithelium and the stroma.¹

CORNEAL CONTOUR DISPLAY

The corneal contour is usually described in one of three ways: qualitative, mathematic, or point-to-point. In the qualitative method, the cornea is said to consist of two zones: a central zone or corneal cap of nearly constant curvature, surrounded by a peripheral zone with an increasingly longer radius of curvature. The corneal cap is an artifact of measurement methods and continues to be used only because it provides a convenient clinical construct. The cornea actually has a radius of curvature that begins to change immediately as one moves away from the apex. Near the apex, the rate of change is slow but increases rapidly toward the periphery. Therefore, the cap diameter depends on an arbitrary criterion for the amount of radius change that can occur before it is considered significant: 1 diopter of change has typically been adopted as a criterion, which yields a corneal cap of approximately 4 mm.^11,12

The second method of describing corneal contour is the mathematic method, which uses expressions such as an ellipse or polynomial. This method is favored by most because it has a number of applications to the optics of the eye, such as the analysis of aberrations. Of the various simple mathematic expressions that can be used to describe the cornea, the ellipse is the best. It is usually possible to align an elliptic curve very closely with radius data from any single meridian or hemimeridian of the cornea. It is only at the corneal periphery that the rate of flattening exceeds that of an ellipse. Thus, for the optic portion of the cornea, the ellipse is an adequate model.^2,11

The third approach is the point-to-point method, which simply consists of an array of corneal radius or power values found at various corneal positions. Although this method seems simple and straightforward, it is difficult to assimilate an overall impression of the corneal contour merely by looking at an array of numbers; however, if all adjacent numbers with the same values are connected, as in contour mapping, the display is transformed into a comprehensible pattern that provides an overall impression of the corneal shape. Currently, the preferred method of displaying the corneal topography by videokeratoscopy is the topographic map. This method provides a large amount of information about the corneal contour in a single display. The corneal topographic map applies the principles of a geographic topographic map, except that instead of representing equal elevations, the isometric zones represent equal radii of curvature. The topographic map is derived from the radius measurements at several thousand corneal positions, which can be displayed in either millimeters of curvature or in dioptric power values. The diopters that are used for corneal power, however have only a relative relationship to the true corneal power in the optical sense. For example if a cornea has a power of 42 diopters at the apex and 40 diopters at some peripheral point, we would expect the peripheral point to be 2 diopters out of focus. With current videokeratoscopy, however, the radius of curvature is actually measured and the power displayed simply represents a conversion from radius to power using the following keratometric formula:

P = (n - 1)/r, where n equals 1.3375.

This formula is not applicable to the peripheral cornea because the keratometric formula is valid only for paraxial rays and becomes increasingly inaccurate as one moves further peripherally. The power used in the calculation of the corneal topographic map is based on the keratometric formula and uses the radius of curvature (AC) ending at the optic axis (Fig. 8).¹¹

Alignment

Currently videokeratoscopes are aligned along an axis that is neither the line of sight nor the visual axis, both of which could be practical reference points. The subject looks at a fixation point on the optic axis of the instrument. The videokerato-scopic axis is aligned perpendicular to the cornea and thus is directed toward the center of curvature of the cornea for some unknown peripheral position (Fig. 9).¹¹

Image Processing

From an optical standpoint the videokeratoscope has no advantage over the photokeratoscope; however, it is superior to the photokeratoscope in terms of image processing. What used to require hours or even days to analyze by hand can now be done in a few minutes. Not only are the measurements faster, they are more accurate. For example with manual digitization, a resolution of 500 lines/frame gives an accuracy of 1.2 diopters; automated digitization statistical procedures can achieve subpixel resolution and an accuracy of less than 0.25 diopters. Formerly it required great skill to construct a photokeratoscope with target rings that were perfectly round so that object size would be the same in all meridians. With the videokeratoscope, the target roundness is immaterial because every meridian can be calibrated separately. The ability of the instrument to measure the curvature of any small area depends largely on the instrument algorithm, which is a series of calculations involved in converting the videokeratoscope image sizes into radius of curvature values for the cornea.²

Software

A reference point is established from which the position of each point can be identified mathematically. Ideally the reference point should be related to an ocular feature such as the visual axis or corneal apex, but because the area of the cornea forming the sharpest retinal image is frequently not centered on any of these landmarks, it is often more appropriate to select the most convenient reproducible reference point. Most systems use the center of the innermost mire, the position of which can be determined in three ways. If the first mire is relatively large, computational techniques must be used to calculate either the centroid of its corneal surface area or its geometrically averaged center. These techniques have been obviated since the development of collimated devices, which can reduce the diameter of the innermost mire to 0.7 mm and use the reflection of the fixation light as the central reference point. The accuracy of the reference center depends on patient fixation and proper alignment of the instrument. Once a central reference point is established, rectangular coordinates are given to each data point where a semimeridian intersects a mire. Most commercial systems have 15 to 38 circular mires and 256 to 360 equally spaced semimeridians, theoretically providing between 6000 and 11,000 data points.

The accuracy of the final reconstruction does not depend on the total number of data points, but on their density as long as the same video pixel is not sampled multiple times.² The rectangular coordinates locating the data points are converted to polar coordinates on the keratoscope mires to facilitate corneal reconstruction. A reconstruction algorithm is then applied to the location of each point on the two-dimensional reflection to give the three-dimensional position of the cornea from which that reflection originated. The algorithm consists of a mathematic formula from which the curvature of the anterior corneal surface is calculated. This is then converted to total corneal power by the standard keratometric index.² Because there is no known mathematic formula that describes the shape of the normal cornea, the algorithm gives only an approximation of corneal shape, which is most accurate centrally where the cornea is most spheric. For each point on mire reflection to correspond to a unique position for the cornea, the following assumptions about the cornea are made: the surface is spheric within the small area being measured, the surface is of uniform refractive index, and the centers of curvature for all reflecting points are on the optic axis. Algorithms are derived in several ways. In the one-step curve-fitting method, the geometry of the reflected mires is globally fitted to a polynomial. A refinement fits the global geometric model to the cornea at each meridian individually, with allowance for local nonconformance. The one-step profile method normalizes the central radius of curvature to a standard 7.8 mm and then uses a successive approximation method to calculate the corneal shape in the periphery in a given meridian.

A more accurate reconstruction of the central cornea is obtained by the two-step profile method, which compares the diameters of individual keratoscope mires reflected from the cornea with those from calibration spheres.²

Accuracy and Reproducibility

The accuracy of any instrument depends on the resolution it achieves at each of its stages between the generation of the mire pattern and the presentation of the data.

The final transverse spatial resolution should ideally be sufficient to detect surface irregularities just large enough to degrade visual function. This precise level still has to be determined and may vary from the center to the periphery of the cornea. Videokeratoscopy measures corneal power with a sensitivity of 0.25 diopters or better within the central 6 mm of the cornea.

Sensitivity is reduced toward the periphery for very steep (greater than 46 diopters) corneas or for very flat (less than 38 diopters) corneas as well as in the presence of marked surface irregularity.^13–17

NORMAL CORNEA

Before we can recognize how disease states are depicted by videokeratography, it is important first to understand the shape of the normal cornea. The normal cornea is aspheric, being steeper centrally and flattening toward the periphery (Fig. 10).

The degree of flattening may vary from 1 to 4 diopters. There is significant variability in the shape of videokeratographs of normal eyes, with 5 to 10 classifiable shapes proposed depending on which scale is used.^18,19 The same normal cornea may also look different if printed in the normalized scale as opposed to the absolute scale. To get an appreciation of normal shape, it is recommended that one scale, the absolute scale, be consistently used initially for diagnostic purposes. In this scale, the color red (range, 49 to 50.5 diopters) is almost never seen in the normal cornea.^19–21 Though there are interindividual differences in corneal shape, the corneal surface shapes of the companion eye in a single patient are often strikingly similar.

ASTIGMATISM

Regular

Regular astigmatism is either congenital or surgically induced and is depicted as a figure-eight pattern (Fig. 11), with the two lobes being almost equal in size. Regular astigmatism may be with the rule (figure eight at 90°), against the rule (figure eight at 180°), or oblique (figure eight at an oblique axis).¹

Irregular

In irregular astigmatism, the major steep radial axes above and below the visual axis are not separated by 180° and there may be multiple zones of increased or decreased surface corneal power, depending on the cause of the astigmatism (Fig. 12).

Causes of irregular astigmatism are multiple and may include tear film abnormalities, as is seen in patients with keratitis sicca or severe meibomitis, the latter of which is depicted on videokeratography as absent areas of digitization and irregular or defocused keratoscopic rings. Epithelial abnormalities are another source of irregular astigmatism and may be caused by diseases such as infectious keratitis, toxic epitheliopathies, map-dot-fingerprint dystrophy, Reis-Bucklers' dystrophy, and lattice dystrophy. The topographic alterations are commonly the result of focal elevations of the epithelium over dystrophic tissue or subepithelial scarring from previous epithelial erosions.

If the irregular astigmatism is the sole source of the patient's decreased vision, the acuity should improve with a rigid contact lens overrefraction, since the lens provides a smooth anterior refracting surface that neutralizes the surface irregularity.

Other causes of irregular astigmatism include inflammatory processes affecting the stroma, trauma, peripheral limbal masses (e.g., limbal dermoids), and pterygia, all of which can cause significant reduction in visual acuity. In these cases, the cornea may appear normal on clinical examination, whereas videokeratography reveals typical and obvious topographic alterations.^1,16

KERATOCONUS

The corneal topography of keratoconus is highly complex and extremely variable, the cone taking many different shapes and the apex being located at variable points relative to the center of the cornea. Before the introduction of computer-assisted videokeratography, cones were described as having two basic shapes: oval and nipple-type. These could easily be differentiated with slit-lamp microscopy and the nine-ring photokeratoscope. Videokeratography has demonstrated that corneal shape is more complex than previously described.^22–24 Classically, keratoconus is depicted as a localized area of increased surface power surrounded by concentric zones of decreased surface power (Fig. 13). The area of steepening may occur anywhere on the cornea. Inferior steepening, more prominent temporally, is the most common pattern seen. Other complex patterns, such as central steepening with a superimposed asymmetric bow-tie pattern are also noted.

Videokeratography is useful in distinguishing keratoconus from other thinning disorders, such as pellucid marginal degeneration and Terrien's marginal degeneration. In pellucid marginal de-generation, videokeratographs have a butterfly-shaped pattern, demonstrating low corneal power along the central vertical axis, increased power as the inferior peripheral cornea is approached, and high corneal power in the midperipheral cornea along the inferior oblique meridians²⁵ (Fig. 14). In Terriens' marginal degeneration, there may be a variety of patterns depending on areas of involvement; however, located superiorly, it will have an inverted butterfly-shaped appearance (i.e., the wings of the butterfly flipped upward and pointing superiorly).²⁶

One of the most useful applications of computer-assisted videokeratography is the detection of keratoconus before the onset of slit-lamp findings or retroillumination techniques. Even in the presence of regular keratoscopy mires, there may be subtle signs of keratoconus as displayed by the color-coded videokeratographs. In most instances the topographic findings in these eyes are similar but more subtle than those in advanced disease; even in these early stages of keratoconus there may be significant variation in the topography of the cornea.

Because it is important to detect abnormal topography before embarking on any refractive surgical procedure, videokeratography is now being used routinely to screen patients for these procedures.^27,28 Since it may be difficult to interpret subtle changes resembling keratoconus on the videokeratograph, quantitative indices are currently being developed by Rabinowitz²⁹ and Klyce to assist the clinician in detecting abnormal topography on an automated basis.³⁰ The Rabinowitz indices Central K and I-S value, which are descriptive of central steepening and inferior dioptric asymmetry, were derived from a study of a large group of normal subjects and keratoconus patients and were based on the fact that the corneas of keratoconus patients are either centrally or inferiorly steeper than normal corneas. The Klyce system looks at multiple indices and uses discriminant analysis and a classification tree to describe the likeness of a videokeratograph to keratoconus videokeratographs, which is expressed as a percentage (Fig. 15).²⁹ Work is in progress to refine both systems.

Videokeratography studies have provided evidence to suggest a genetic basis for keratoconus. In one study,³¹ we found that 50% of family members of patients with keratoconus had subtle topographic findings similar to that seen in clinically obvious keratoconus. In a subsequent study,³² using videokeratography as an aid to construct family pedigrees, we demonstrated an autosomal-dominant mode of heredity (Fig. 16). Future investigations of suitable family pedigrees for genetic linkage analysis may provide pointers to the pathogenesis of this disease at a molecular level.³²

PENETRATING KERATOPLASTY

Videokeratography has several clinical applications for penetrating keratoplasty. First, in planning surgical treatment for keratoconus, the extent of the ectasia can be mapped out. Second, if pellucid marginal degeneration is detected in a patient suspected of having keratoconus, the surgeon might want to consider embarking on a lamellar procedure before considering a full-thickness keratoplasty. Postoperatively, the degree of astigmatism can be monitored. In patients who have continuous running sutures, videokeratography can aid the clinician in adjusting the running suture to decrease the amount of astigmatism. In patients who have interrupted sutures as part of their procedure, videokeratography can delineate which sutures are tight and should be removed during selective suture removal.^33–35 Finally, videokeratographs can assist the surgeon in planning for astigmatic keratotomy in patients who have large degrees of postpenetrating keratoplasty astigmatism. Whereas keratometry might suggest that T cuts should be placed 180° apart, videokeratography often demonstrates that the steep axes are nonorthogonal, influencing the surgeon to place the T cuts in the steepest areas, which might be separated by angles of less than 180°. A recent study of patients with postpenetrating keratoplasty astigmatism showed that the results of astigmatic keratotomy combined with compression sutures using videokeratography as a guide are superior to the results of studies in which either keratometry or photokeratoscopy alone were used as a guide.³⁶

RADIAL KERATOTOMY

Videokeratography in radial keratotomy has gained increased utility in the following areas: screening before surgery, planning for surgery, monitoring corneal changes after surgery, explaining untoward effects of surgery, and managing complications.^37–41 As previously discussed, preoperative screening of candidates for radial keratotomy is useful to rule out early forms of corneal ectasia not detectable by clinical means and also holds promise for predicting the outcome of surgery based on corneal shape. Previous studies suggest that corneal shape might be a predictor of the response to radial keratotomy. Videokeratography is extremely useful for planning astigmatic surgery in conjunction with radial keratotomy. The topographic pattern is useful for deciding the placement and length of the astigmatic cuts; the pattern and location of the astigmatism may also dictate the orientation of the radial cuts. Color-coded maps might also be useful in planning repeat surgery in patients with a response to surgery that has been less than optimal. A wire mesh profile in the new Topographic Modeling System software demonstrates the location and depth of the cuts. Cuts that have not been made deep enough for maximal effect can be identified and redeepened for additional effect (Fig. 17).

EXCIMER LASER PHOTOREFRACTIVE KERATECTOMY

When excimer laser photorefractive keratectomy becomes approved in the United States, it will be essential for the clinicians performing these procedures to have a thorough understanding of videokeratography. Videokeratography is not only essential for screening candidates for these procedures, but it also provides important information regarding the quality of the ablation zone, the diameter of the ablated zone, centration of the ablation, and the stability of the topographic alterations. In addition, irregularity and multifocality within the ablation zone can be determined. Decentration of the ablation zone, as determined by videokeratography, might explain postoperative halo or glare effect. Irregular ablation zones (as is seen in “central islands”) often explain decreased acuity and decreased quality of vision after these procedures (Fig. 18). Recognition of these abnormal zones has resulted in modification of the procedure to prevent their occurrence.^42–46

CONTACT LENSES

Before evaluating a videokeratograph, it is critical to determine whether the patient is a contact lens wearer, what type of contact lenses he or she wears, and how long the lens was out of the eye when the videokeratograph was performed. Normal contact lens wear is likely the most common cause of alterations of corneal topography. Topographic changes are more common with rigid polymethylmethacrylate and rigid gas-permeable contact lenses, but they may also occur with daily- and extended-wear soft contact lenses. Topographic alterations induced by contact lens wear are characterized by a frequent reversal of the normal topographic pattern, evident as a progressive flattening of the corneal surface from the center to the periphery, a loss of radial symmetry, and a central irregular astigmatism.

In corneas subjected to decentered rigid contact lens wear, there is frequently a correlation between the most common resting position of the contact lens and the corneal topography. In these eyes, there is usually relative flattening beneath the decentered contact lens and relative steeping of the corneal contour outside the area of contact with the decentered contact lens.^47–49 Contact lens—induced alterations of corneal contour should be excluded before refractive surgical procedures are considered. Videokeratographs of contact lens wearers simulate—and are often indistinguishable from—topographic abnormalities seen in keratoconus. Before surgery can be undertaken in these patients, contact lens wear should be discontinued and topography monitored until it is normal and stable.²⁷

Contact lens wearers sometimes show signs of corneal warpage on corneal topography. Symptoms include decreased visual acuity with eyeglass wear and, infrequently, intolerance to contact lenses. The time required for resolution of corneal warpage after discontinuation of contact lens wear varies from patient to patient. Topographic changes frequently resolve in wearers of soft contact lenses within 6 weeks of discontinuing lens wear. In wearers of rigid contact lenses, however, the time required may vary from 1 month to more than 8 months. The topography must be monitored by computerized topographic analysis until there is a return to a normal and stable corneal contour.⁴⁷ Because videokeratography provides important information about corneal curvature in the periphery of the cornea, it is showing promise as an aid to contact lens fitting in complex corneal topographies, such as keratoconus and post-radial keratotomy patients.^50,51

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