Ординатура / Офтальмология / Учебные материалы / Orthokeratology Principles and Practice 2004

18 ORTHOKERATOLOGY

Table 2.1 Expected accuracy of central radius of curvature measurements asderived by Stone (1962)

ultimately on their accuracy, repeatability, and ease of use. The accuracy of an instrument may be defined according to the tolerance that is expected when the instrument is to be used for a clinical function. For purposes such as contact lens fitting, Stone (1962) has stated that the radius of curvature should be measured within ± 0.02 mm. Table 2.1 shows how the expected accuracy of radius of curvature was derived by Stone (1962).

In addition, repeatability may be defined as the ability of an instrument to reproduce the same measurement on two independent occasions when no change in the structure to be measured has taken place.

HISTORICAL OVERVIEW

The first development in the assessment of gross corneal topography was the keratoscopic disk by Placido in 1880. This simple hand-held instru-

Figure 2.1 Placido disk concentric ring target.

ment was used for observation rather than actual measurement of corneal contour (Fig. 2.1). The following valuable information may be derived from the Placido disk:

•corneal toricity

•the approximate location of the principal meridians

•gross changes in shape

•localized surface irregularities

•the approximate position of the corneal apex with respect to the line of sight.

Information of this nature would be of great use in clinical practice, particularly if a hard copy could be made, such as a photographic recording. Gullstrand (Ludlum et al 1967) was one of the first investigators to introduce the photokeratoscope. Many new designs have emerged - all of which have attempted to measure a larger area of the cornea by using various shaped targets. Gullstrand used a plane object surface, which prevented larger areas of corneal surface being measured. Nevertheless, he found that the normal individual had a smooth corneal surface that flattened away from the corneal apex. Later, using a flat object of tangential design, measurements of up to 7 mm in diameter were obtained (Fincham 1953). Knoll et al (1957) used a hemispherical or cylindrical object surface that enabled an area of 10 mm of corneal surface to be measured. The advantage of using an object of hemispherical design was that the size of the target was much reduced, thus making the instrument less bulky (Fig. 2.2).

Ludlum et al (1967) considered the limitations of photokeratoscopes at that time. Three suggestions were made from their study:

•The image plane (located behind the cornea) should be flat. This point is particularly important with respect to the design of a target for the following reason: if the image lies on a curved image plane, then there will be one point of focus on the flat plane of the photographic film. Ludlum et al (1967) found that, for an ellipsoidal target surface, the image from a spherical reflecting surface lay on a flat plane.

•The analysis of the data should be detailed and accurate. Numerous methods have been adopted to calculate the parameters describing

Figure 2.2 The difference in area of corneal surface measured for a plane target and a hemispherical target.

the corneal profile; the various techniques are discussed later in this chapter.

•There should be accurate and reproducible alignment of the patient's line of sight with that of the instrument. Accurate alignment is necessary in order to position the vertex normal of the cornea (that point on the corneal surface that is perpendicular to the keratoscope axis when the subject is viewing the fixation target) relative to the line of sight.

More recently, computers have been used to analyze the data supplied from the photographic image of the corneal surface. Known as computerassisted videokeratoscopes, these instruments have been used for clinical applications such as contact lens fitting and corneal screening for refractive surgical procedures.

Bibby (1976) stated the technical requirements for reliable topography measurement as follows:

1.The units to describe corneal topography must be independent of the shape being measured.

2.The instrument should measure the total area of interest.

3.All information should be acquired simultaneously.

4.The technique should have high accuracy and reproducibility.

CORNEAL TOPOGRAPHY AND ITS MEASUREMENT 19

If one accepts the above technical requirements, then it is possible to assess the suitability of other techniques. Thus, applying the first requirement, instruments such as the keratometer only measure central radius of curvature and assume that the surface being measured is spherical. This is not true for the cornea that has been shown to be best approximated to a conic section (Bibby 1976, Guillon et al 1986). Furthermore, keratometry does not fulfill the second requirement, because only the central 3 mm of the corneal surface is measured. In order to resolve larger areas of the cornea, the keratometer requires the use of an accessory device (the topogometer), which involves repeated measurement, and the additional inaccuracy of asking the patient to alter fixation to another point.

Various modern corneal topographic systems are now available. A description of some of the more widely used systems will now be presented.

Computer-assisted videokeratography combines the principle of keratoscopy with computerized image analysis and data processing using personal computers (Gormley et al 1988). Examples of commercially available systems and their respective technical details are summarized in Table 2.2.

With the development of computer hardware in terms of processing speed and storage capacity, the number of points analyzed on the corneal surface has increased dramatically. The number of rings and points of analysis are chosen in order to provide adequate resolution of the corneal surface (Table 2.2). Images obtained from the videokeratoscopes are digitized and topographic data points are extracted in polar coordinates. Various forms of presentation of these data are available, such as color-coded dioptric maps, Placido images, wire mesh and solid models and elevation maps, to mention but a few.

A significant amount of research has taken place regarding the accuracy of modern computerassisted keratoscopic devices on test surfaces (Hannush et al1989, 1990, Koch et al1989, 1992).

Table 2.2 The principal features of currently available commercial topography systems. The orthokeratology pluses and minuses represent the authors' experience in the use of these topographersfor orthokeratology (OK).

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The results show an acceptable level of accuracy and reproducibility. Hannush et al (1989) found measurements to be within 0.5 D in 76% of the readings on human corneas for rings 2 through to 13 for the Topographic Modeling System 1 (TMS-l). In a study by Koch et al (1992), the mean absolute differences between the keratometer and the EyeSys in terms of power were 0.19 D and 0.21 D for the steep and flat meridians, respectively. Tsilimbaris et al (1991) found a clinically significant difference between the EyeSys and [aval keratometer when measuring astigmatic eyes with a cylinder greater than 1.50 D. A mean difference of 0.84 D was found, but only 18 eyes were measured. Tsilimbaris et al (1991)suggested that a possible explanation could be poor focusing on one of the two astigmatic meridians.

Antalis et al (1993) compared the EyeSys (CAS) and the TMS-l in terms of central corneal curvature in 18 eyes with a variety of corneal conditions. The average differences for the two instruments were -0.2 ± 0.7 D for the flat central meridian and -0.7 ± 0.9 D for the steep central meridian. Correlation coefficients for the two instruments were 0.9901 and 0.9937 for the flat and steep meridians, respectively. Both instruments were also found to correlate relatively well with the keratometer (correlation coefficient, r = 0.9617 and 0.9844 respectively). However, the use of correlation coefficients to compare the agreement of instruments is not an appropriate statistical test as it merely shows the level of association. Bland & Altman (1986) suggested that a plot of the difference of the two readings versus their respective means is a more accurate method.

Jeandervin & Barr (1998) compared the repeatability and accuracy of four commercially available topographers (Alcon Eyemap, EH-290, EyeSys 2000, and Humphrey ATLAS) in 10 optometry students. Two independent repeat measurements of the right eye were taken to evaluate repeatability, whereas precision was evaluated using four calibration spheres. Although there was no statistically significant difference for the four topographers, the EyeSys had the greatest repeatability, followed by both Humphrey instruments. Greatest accuracy was observed with the ATLAStopographer.

With respect to the preclslOn of Placido systems for abnormal corneas, McMahon et al (2001) compared the test-retest reliability of three commercially available Placido ring videokeratoscopes in subjects with keratoconus. Nine subjects (16 eyes) had up to four images per eye generated in random order from the EyeSys II, Dicon CT-200, and Keratron. The short-term variability was 0.61-3.31 for the Dicon, 0.94-1.51 for the EyeSys, and 0.58-2.85 for the Keratron with respect to axial curvature. For measurements of instantaneous curvature, the variability was 1.07-6.82 for the Dicon, 0.79-1.77 for the EyeSys, and 1.23-3.03 for the Keratron. The authors concluded that their results supported the notion that Placido devices have reduced repeatability when measuring corneal irregularities.

Unfortunately, there are limitations of the keratoscopic approach in the analysis of corneal shape. Firstly, as already stated by Ludlum et al (1967), the image of the target mires should lie on a flat plane. Even with the modification of the target plane, it is not possible to achieve this for all corneas because of the large variety of normal corneal shapes. Thus, there could be errors induced from poor focus of different rings. Secondly, it has been shown that slight decentration of the alignment and focus results in large errors in actual measurement (Nieves & Applegate 1992). Thus, various modifications in the design of instruments have a role in reducing errors due to poor focus and misalignment.

DESIGN FACTORS

Working distance

Working distance, mire size, and the size and position of the reflected mire image are all intimately related. For example, as working distance decreases, the influence of instrument alignment error will increase (Nieves & Applegate 1992, Antalis et a11993); however, the influence of facial anatomical factors is reduced, so enabling a larger area of the cornea to be measured. Using a micron positioner (a device used to position a test surface accurately with respect to the videokeratoscope axis), Nieves & Applegate (1992) determined the effect of working distance on the accuracy of meas-

urements found with the TMS and EyeSys videokeratoscopes for two acrylic spheres (r = 7.1153 mm and r = 7.9497mm). The results showed that the EyeSys (which has a larger working distance) consistently measured the sphere to a higher degree of accuracy than the TMS-1 for both frontal plane (x- and y-axis) and axial (z-axis) misalignment. Applegate (1992) pointed out that the working distance chosen by the manufacturers of the EyeSys (Model I) and TMS-1 probably represents two extremes of realistic values.

As a general rule, instruments that use large working distances, which are less susceptible to focusing error, will also have large Placido designs (Fig. 2.3). Conversely, smaller Placido designs (often referred to as cone designs) will be associated with smaller working distances. With the improvement in auto alignment and focusing systems, manufacturers are tending to use smaller cone-type Placido rings that permit greater corneal coverage.

Defining a reference point for corneal modeling

Irrespective of manufacturer design, all videokeratoscopes at present use the same alignment

Figure 2.3 Large Placido mire.

CORNEAL TOPOGRAPHY AND ITS MEASUREMENT 25

principle (Mandell 1992). The subject views a luminous fixation point, the image of which is viewed by the practitioner on the monitor. At this point, the subject's line of sight is coaxial with the instrument axis. Finally, the practitioner must then center the reflected image of the luminous markers with respect to a reference marker on the monitor. The final stage of alignment fulfills one of the assumptions and criteria for videokeratoscopy - that the instrument axis should be perpendicular to the cornea. The consequence of the alignment procedure is that the instrument axis may be perpendicular to an undefined point on the cornea. Figure 2.4 shows the point of alignment with the cornea when the conventional procedure of alignment is performed.

Although, after alignment, the optic axis of the instrument is perpendicular at a point on the cornea and is directed therefore towards the instantaneous (tangential) radius of curvature, measurements are performed from an eccentric and unknown point. The point on the cornea from where measurements are performed with present videokeratoscopes is unique. Mandell (1992) suggested that from a clinical and functional viewpoint, the ideal reference point would be the intersection of the line of Sight with the corneal surface. Manufacturers of most videokeratoscopic systems are now able to locate the entrance pupil on dioptric maps. Mandell (1992) described a simple modification to conventional videokeratoscope alignment where measurements are centered about a unique point on the corneal surface where the line of Sight and the instrument axis intersect. This point is not as peripheral on the cornea as with conventional alignment procedures. Figure 2.5 summarizes the modification as described by Mandell (1992).

Figure 2.4 shows that, from the videokeratoscope view, the monitor reference pattern will be displaced away from the center of the entrance pupil. The reason for this is that the instrument requires the optic axis of the instrument to be perpendicular to the corneal surface. In Figure. 2.5, the subject is asked to view an eccentric target so that the monitor reference pattern of the videokeratoscope is placed in the center of the entrance pupil as viewed in the monitor. Once this has been accomplished, the luminous fixation marker

26 ORTHOKERATOLOGY

is then aligned with the monitor reference pattern. After alignment in this manner, the line of sight and the optic axis of the videokeratoscope intersect at a unique point on the cornea and measurements are centered about a point where the line of sight intersects the cornea.

More recently, Hubbe (1994) evaluated the effect of alignment of the EyeSys CAS in five corneas and three aspheric test surfaces of varying radius with the line of sight directed at 2'so, 5°, and 10° below the videokeratoscope axis (the instrument axis was still perpendicular to the surface under test). Hubbe (1994) found that a 5° deviation from the fixation source, a significant

(P < 0.05), occurred. Furthermore, the color-coded maps mimicked the appearance of keratoconus. Hubbe (1994) concluded that accurate alignment with the line of sight is important as misalign-

Figure 2.4 The position of the various reference points and axes after alignment has been performed. Eand fare entrance and exit pupils, respectively, Cis the centerof curvature of the cornea. The videokeratoscope axis is aligned with an unknown point on the cornea. Reproduced with permission from Mandell (1992).

Figure 2.5 Alignment proposed by Mandell (1992) in order to align the videokeratoscope axis with the line of sight at the corneal surface. For abbreviations, see Figure 2.4.

ment can induce errors in the subsequent calculations to determine corneal topography.

Focusing systems

User errors can only be attributed to alignment inaccuracy. The importance of accurate z-axis (i.e., along the instrument axis) alignment has been shown to be critical in the accurate measurement of corneal topography (Mandell 1992, Nieves & Applegate 1992). Mandell (1992) found that the impact of z-axis alignment error on corneal radius derivation was greater with instruments that operated at shorter working distances. Using the EyeSys and the TMS videokeratoscopes (the EyeSys has a longer working distance than the TMS), Mandell (1992) found that the effect of z-axis defocus was greater with the TMS than the EyeSys. Nieves & Applegate (1992) confirmed these results in a similar study using the same instruments.

Manufacturers also attempted to redesign instruments in order to minimize errors due to z-axis misalignment. The MasterVue Smart Topography system (now known as the ATLAS topographer) incorporated a dual-camera system that enabled the operator to view a magnified image of the centrally reflected rings as well as the overall cornea. Theoretically, z-axis errors reduce because of the smaller depth of focus obtained using the second higher-magnification camera. Figure 2.6 shows how the dual-camera system operates.

Image editing

The ability to edit captured Placido ring images forms an important aspect of corneal topographic accuracy. Facial contours can interfere with the Placido mires. Figure 2.7 illustrates how a digitally captured Placido image, if unedited, would result in errors in the nasal area of the image. The Humphrey topographer provides two chin-rests so that patients can turn their face in order to reduce nasal shadowing. Practitioners performing procedures such as orthokeratology must take the time to analyze these Placido images and make the appropriate corrections to the computer digitization. Other factors such as long lashes are

also frequently responsible for loss of data in the superior area of the cornea. Variability in the tear film due to excessive lipids can also interfere with the shape of the reflected Placido mires. Asking the patient to blink several times to dissipate some of the lipids can help but, rather than introduce further inaccuracies, practitioners would be wise simply to delete any suspect areas.

Rasterstereography andscanning slit topography systems

Rasterstereography was initially used for the measurement of corneal topography by Bonnet & Cochet (1962). The principle involves projecting a grid of light on to the corneal surface. As the cornea is transparent, the technique involves rendering the cornea opaque. Originally, talcum

CORNEAL TOPOGRAPHY AND ITS MEASUREMENT 27

Figure 2.6 The MasterVue dual-camera system used to obtain accurate z-axis alignment (reproduced from MasterVue literature).

powder (with the use of a suitable anesthetic) was used to form a real image of the target. The use of talcum powder to make the cornea opaque was the major drawback of this technique.

More recently, this method has attracted more popularity as talcum powder has been replaced with sodium fluorescein. The mechanics have been concisely described by Arffa et al (1989): a projected grid of light is used to illuminate the cornea and then viewed at a specific angle from the projection source (Fig. 2.8). The whole system is incorporated on a Zeiss stereo photo slit lamp. Image acquisition involves focusing the slit lamp on the corneal surface; when in focus, a flash is triggered which provides the required intensity for image analysis. The flashlight passes through the cobalt blue excitation filter causing the projected grid pattern to fluoresce. The image is then

Figure 2.7 Incorrectdigitization induced by nasal shadow. If unedited, this image will result in pooraccuracy of the measurement of the cornea.