The rotating mask is a valuable alternative to the iris diaphragm when performing excimer laser photorefractive keratectomy (PRK). By adopting a suitable shape for the mask aperture, the exposure time of different sections of the underlying surface can be controlled selectively. The exposure time of a given point situated at a radius r from the center is directly proportional to the aperture angle of the mask at this radius. In this manner, any exposure profile with circular symmetry can be generated.1 Rotating masks are valuable in the performance of PRK for hyperopia.2,3
The ablation profile for a hyperopic correction requires a smooth transition zone to prevent an abrupt step at its peripheral edge. An abrupt step would cause compensatory healing responses, resulting in regression of the implemented correction.3,4 Two ablation profiles that fulfill this requirement were calculated. They have a central steeper zone with a diameter of 4 mm and a smooth transition zone that is either 1 or 2-mm wide. The ablation profiles are "4-mm/6-mm" and "4-mm/8-mm" depending on the diameter of the theoretical optical zone and the total ablated area. The details are described in our other paper in this issue.5 The transition zone is an area of flattening in order to obtain central steepening: the axial power shows a dip, but is- by definition- always convex with a positive power. This is in contrast to the instantaneous power. For a +10 D correction with the 4-mm/6-mm profile, the instantaneous radius of curvature (ROC) and power are negative in the transition zone. This zone is, in fact, a concave ring surrounding the topographie optical zone. The same correction with a 4-mm/8-mm profile results in a very flat (radius of curvature up to 47 mm, 7 D), but not concave transition zone.
The following factors have an influence on power profiles in vivo:
1. Ablation profiles
2. Energy distribution of the laser spot (affecting the local ablation rate)
3. Asphericity of the cornea
4. Physiologic growth of the cornea
5. Epithelial and stromal healing responses
The induced axial power profile is defined as the expected axial power profiles in vivo with all but the healing factors (epithelial and stromal healing) taken into account. This power profile is equivalent to the axial power profile as it would be found after ablation of an inert surface with the same ablation characteristics and aspheric topography as the cornea. Our first aim was to calculate the induced power profiles " as exactly as possible. This is an unusual step in PRK experiments because details of ablation algorithms are not usually published.
Our second aim was to measure the power profiles in vivo. The comparison of induced and measured power profiles should help clarify how healing mechanisms modify ablation profiles.
A third aim was to see whether a broader transition zone of 2 mm was more effective in preventing regression than a narrower transition zone of 1 mm. Stabilization of corneal topography is known to take several months. Originally, an observation period of 12 months was planned. However, the treated corneas turned out to be particularly challenging for videokeratography. This led to an extension of the observation period and a comparative study of the performance of videokeratoscopes on mixed concave/convex surfaces. This aspect will not be reported in detail.
MATERIALS AND METHODS
Two masks were designed and manufactured for the two ablation profiles (4-mm/6-mm and 4-mm/8mm). A Barraquer-type suction ring (Aesculap Méditée, Heroldsberg, Germany) was adapted and equipped with a mask holder that rotated on air bearings. Three silicone tubes (4-mm diameter) were attached to the device to apply a vacuum for suction fixation to the limbus, to power the turbine drive, and to evacuate the ablated products around the ablation site. The suction ring was positioned on the limbus for an unobstructed view of a 12-mm diameter of the corneal surface. After proper centering, the mask holder was installed. An air flow between 5 and 10 liter/min yielded rotation speeds between 500 and 1000 cycles/min, measured by a stroboscopie meter. The masks rotated 1.5 mm above the cornea. The total weight of the device was 50 g. The laser was a Questek type 2620 equipped with a beam homogenizer (Exitech, Oxford, UK). The homogeneity was controlled by recording the fluorescence induced on a glass plate with a videocamera. The image was digitized and analyzed by means of a computer program developed for this purpose by one of the researchers. The intensity of the beam was distributed in a circular symmetric fashion, decreasing 20% toward the edge of the 8-mm diameter region. The average flux density in this 8-mm area measured with a joulemeter (Questek, Billerica, Mass) was 60 mJ/cm2. Based on our ablation rate versus flux density diagram, the ablation rate was estimated to be 0.05 µt? per shot, corresponding to measurements on bovine corneal stroma.6 The low ablation rate seemed to yield a smooth ablation bed. The laser was fired at a rate of 10 Hz.
Both ablation profiles were tested on the eyes of four Dutch belted rabbits (total eight eyes). Two other rabbits (four eyes) of the same breed were untreated for comparison to observe the natural evolution of the corneal contour by aging. The rabbits were anesthetized with a subcutaneous injection of 2 ml of fentanyl/phenobarbital. Black silk 6-0 sutures were sewn in the eyelids to hold them open. Mechanical removal of the epithelium was followed immediately by the excimer laser treatment. The left eyes received the 4-mm/6-mm correction with the 1-mm transition, the right eyes the 4-mm/8-mm correction with the 2-mm transition. All eyes were exposed for a +10 D correction in the corneal plane, using 1340 pulses for the 4-mm/8-mm mask profile and 1210 pulses for the 4-mm/6-mm mask profile. At the completion of irradiation, four of the eight rabbit corneas were irrigated with a 0.5% solution of dichlorotriazinyl aminofluorescein (DTAF, Gibco) dissolved in 0.2 M sodium bicarbonate. After 30 seconds, the excess dye was washed from the wound with phosphate buffered saline. (The animals were still alive at the time of -submission of the paper. The histology will be presented in a subsequent paper.) Apart from an antibiotic ointment and a single subconjunctival injection of betamethasone phosphate/acetate, no topical medication was given.
Corneal topography was measured with an EyeSys videokeratoscope (software version 2.00-4), before surgery and at 3, 10, 20, 30, 40, 50, 65, 75 and 120 weeks after surgery. The rabbits were sedated slightly with a subcutanous injection of 0.5 ml of fentanyl/phenobarbital. Accurate centering of the treated zone in the videokeratoscope was possible due to the presence of a very broad ring (usually the fourth or fifth) corresponding to the flat transition zone. The eye was tilted until this ring was concentric. The measurement of the rabbit eye was always done by the same researcher (HD). Several images were taken until focusing and centration were optimal. The processed Placido images were checked for accurate edge detection and obvious mistakes were corrected. Placido images were saved. Calibration of the machine was repeated on several occasions. The mean central power was determined from the EyeSys profile graphs as the power halfway between the steepest (red) and the flattest (blue) semimeridian in the center of the correction. The resolution of this measurement was half a diopter. On the same profile graphs, the central astigmatism and the mean power was determined at eight increasingly eccentric points (0.5; 1.0;... 4.0 mm). The maximal rates of change of axial power were measured graphically by drawing a line tangent to the steepest part of the slope on the profile graphs. On the Placido images, the middle of the broad ring was considered to be the middle of the transition zone. The distance to the center was measured on the four principal meridians and averaged for each cornea. The videokeratoscope used an index of refraction of 1.3375 to calculate corneal power. Unpaired Student t tests were used to compare mean changes in central power and other parameters.
Figure 1. Induced power profiles of the 4-mm/8-mm (A) and 4-mm/6-mm (B) diameters. They take into account the original ablation power profiles, the laser beam energy distribution, the prolate shape of the cornea and the growth of the eye. These power profiles are expected if no healing processes modify the surface after ablation. (The horizontal line is a reference sphere of 47 D).
Induced Power Profiles
The mean central power (12 eyes) before surgery was 47.20 (±0.90) D. All corneas were prolate with a mean flattening of 2.00 (±0.50) D at the 4-mm eccentricity. The mean central power of the four untreated eyes after 2 years was 43.50 D. Due to the physiologic growth of the eyeballs, the corneas flattened 3.75 (± 0.75) D.
Figure 2. The ablation bed immediately after surgery appeared smooth. The unablated central zone and the depression of the transition zone are evident.
Taking into account the 20% loss of laser beam intensity at the edge, the induced power profiles after 2 years were calculated based on the original ablation profiles (Fig 1). The expected diameter of the zone with homogeneous (± 1 D) power is only 2.6 mm instead of the originally intended 4 mm. The characteristic midperipheral flattening and resteepening remain apparent.
Figure 3. (A) Placido image of a 4-mm/8-mm correction and (B) its profile graph. The fourth black and the fifth white ring are markedly broadened and correspond to the transition zone (65 weeks after surgery).
Figure 4. (A) Placido image of a 4-mm/6-mm correction and (B) its profile graph. The broad white ring is obvious. Note that between 1 and 9 o'clock the peripheral edge of the fourth white ring is imaged twice by the cornea (arrow). This double reflection increases the number of white rings from eight to nine. The focusing cross at 9 o'clock in the fourth white ring has also a double image (30 weeks after surgery).
Topography and Power Profiles in Vivo
The ablation bed immediately after surgery had a smooth appearance (Fig 2). A small non-ablated area was visible centrally and in the periphery the transition zone could be easily recognized. Reepithelialisation was complete after 3 to 5 days. Figures 3 and 4 show typical Placido images of a 4mm/8-mm correction (65 weeks after surgery) and a 4-ram/6-mm correction (30 weeks after surgery) with corresponding profile graphs. On these Placido images, the broad ring, intuitively corresponding to a flatter transition zone, was striking. This ring was situated more peripherally in the 4-mm/8-mm corrected corneas than in the 4-mm/6-mm corrected corneas. The mean distance from the center to the middle of the broad ring (transition zone) was 2.89 (±0.05) mm in the 4-mm/8-mm ablated corneas and 2.49 (±0.05) mm in the 4-mm/6-mm ablated corneas. The difference is statistically significant (p<0.005). Peripheral to this broad ring, the rings were typically narrower, intuitively corresponding to the steepening in the peripheral half of the transition zone. Beyond this, apparently normal rings were visible corresponding to the untouched peripheral cornea.
The corresponding power profile graphs showed a central steep zone. Figure 5 shows the increase of the mean central power for the 4-mm/8-mm and the 4-mm/6-mm ablated corneas. The initial power increase of the 4-mm/8-mm treatment was +12.10 (± 3.40) D, and +13.40 (±3.70) D in the 4-mm/6-mm treatment. After 2 years, the residual increase in mean central power not corrected for physiologic flattening was +3.60 (±3.90) D (not statistically significant) and +3.90 (±2.80) D (statistically significant; p<0.05). The regression occurred mainly within the first 3 months after surgery.
From the very first weeks after surgery, the power distribution in the central steep zone was less homogeneous than expected. Indeed, a power "peak" could be observed in all corneas, indicating that they started to flatten immediately paracentrally: between the first and second mire. During the entire observation period this peak pattern persisted (Fig 6), although the height of the peaks diminished. Figure 7 shows the mean (four eyes) power profiles of both treatments. The mean power difference between center and periphery was 9.40 (±2.9) D. This is a significant difference from the preoperative asphericity (p<0.0005). The mean power profile of the 4-mm/6-mm corrections was not significantly different from the mean power profile of the 4-mm/8-mm corrections.
Figure 5. The increase in mean central power for the 4-mm/8-mm (A) and 4-mm/6-mm (B) ablations, respectively.The increases are not corrected for the natural flattening of the cornea during growth. The solid line connects the means of the four eyes. Names of the rabbits correspond to symbols on graph.
Because of this peak pattern, it was difficult to define a topographic optical zone of homogeneous power (±1 D); it was equal to (or smaller than) the area within the central mire of the 0.7-mm diameter. The power decreased in a more or less linear way to reach a minimum peripherally. The average central astigmatism for all eyes was 1.40 D before surgery and 2.40 D at the end of the observation period. Most corneas showed a large amount of rotational symmetry with the flattest and the steepest meridian of the profile graphs closely overlapping (Figs 3, 4 and 6). The maximal rates of change of axial power were 7.5 (± 1.7) D/mm for the 4-mm/8mm corrections and 9.6 (± 1.7) D/mm for the 4-mm/6-mm, significantly (p<0.005) lower than in the induced rates of change of power (15 and 45 D/mm, respectively), but statistically not different one treatment from the other.
On the profile graphs (Figs 3, 4 and 6), as on the mean profile graphs (Fig 7), there was no evidence of a midperipheral flattening nor of a peripheral resteepening as would have been expected from the induced power profiles and from observation of the Placido images. Around the central peak they simply show a flat zone with uniform power around 40 D. This peripheral power corresponded to the nonablated surface and was the same as the peripheral power in the control eyes. Surprisingly, neither flattening nor peripheral steepening were detected in the transiton zone on the profile graphs or on the color maps.
Figure 6. Profile graphs from rabbit Lisette OD before surgery, 10, and 120 weeks after surgery show a stable power peak. This rabbit had the least amount of regression in the 4-mm/6-mm and 4-mm/8-mm corrections.
Figure 7. Mean axial power at eight increasingly eccentric points in the 4-mm/6-mm and 4-mm/8-mm corrections as measured by the Eyesys videokeratoscope. The difference in power profiles between the two types of treatment was not statistically significant.
Figure 8. The peripheral edge of the fourth white ring (left) has a double virtual image behind the reflecting surface of the cornea (right). From the principal rays used to construct the virtual image, only the normal to the reflecting surface is drawn. If from one object point, two different normals to the corneal surface can be drawn, the surface between these two reflecting points cannot be continuously convex; it must be flat or concave.
The Placido image in Figure 4, an example of a 4-mm/6-mm correction, merits a closer look. The fourth white ring is so broad that between 1 and 9 o'clock, its peripheral edge is imaged twice on the cornea. The focusing cross at 3 o'clock is smeared over the entire width of the broad ring, and at 9 o'clock has a double Purkinje image. The central white-to-black transition of this ring was partly recognized and marked with red and/or yellow dots. However, this central ring edge was erased because it would increase the number of rings from 16 to 17, a possibility not foreseen in the EyeSys software. Peripheral to this broad ring, two or three rings were particularly narrow. The far periphery shows the rings reflected from the untreated surface.
We introduce a new definition, the "induced power profile." In photorefractive keratectomy, the Munnerlyn-Misotten equations1,7 have been used as a basis for the ablation algorithms and subsequently modified empirically from the increasing clinical database.8 This means that a certain amount of overcorrection is calculated to compensate for regression. The precise correction factors are not published because they are considered proprietary by the manufacturers. As new ablation methods and algorithms are introduced- such as multiple zone treatments9·10 or aspheric corrections11-the uncertainty about what has actually been ablated from the cornea only increases. The ablation profile in polymethylmethacrylate (PMMA)8 does not give sufficient information to the clinician about the actual treatment. Information on the induced power profiles would lead to better insight into the treatment and the subsequent healing processes.
Few experiments on PRK for hyperopia with a transition zone have been reported.12"14 The technique has not received the attention that PRK for myopia has received. The present experiment in rabbits shows that a central steepening of the cornea with PRK is possible. The predictability and accuracy of the correction, however, do not seem to be very high. A planned correction of +10 D and an achieved correction of +3.60 ±3.9 D and +3.90 ±2.8 is not a spectacular result, and is only significant for 4-mm/6-mm corrections. These results should be corrected for the physiologic flattening that accompanies the growth of immature rabbits. This flattening was 3.75 D.15 However, because of the relatively small number of untreated eyes and because the time course of this flattening (gradual or more pronounced in the young rabbit) was insufficiently documented, this flattening was not calculated in Figure 5. If it had been, both treatments would have shown significant steepening. In addition, photorefractive keratectomy in rabbits is prone to regression, and permanent refractive changes are more difficult to obtain than in humans16; nevertheless, no intentional overcorrection was performed.
The Placido images of the treated corneas showed more similarity than appears from mere central steepening. Figure 5 might give the impression that the topography of several rabbits returned to almost the preoperative status. This was not the case, as the mean axial power profile shows (Fig 7). In all treated eyes, a central power peak was present at the end of the observation period. The relative sta bility of this power peak is ascribed to the presence of a suitable transition zone in the ablation profile. A surprising finding was that the broader 4-mm/8mm transition zone did not "protect" more efficiently the +10 D in the central ablation zone than the narrower 4-mm/6-mm transition zone. The only significant difference between both ablation profiles was the localization of the transition zone on the cornea.
Comparison of the actual (Figs 3,4,6 and 7) and induced power profiles (Fig 1) reveals two major differences. First, the diameter of the central steeper zone with homogeneous power (±1 D) was smaller than induced: 0.7 mm or less, compared to 2.6 mm. The most central mire of the EyeSys had a diameter of 0.7 mm on these steep corneas. The flattening (and the actual transition zone) started paracentralIy. With the single mire of a Bausch and Lomb keratoscope measured at the 1.5-mm eccentricity, the steepening would have remained largely undetected, illustrating the value of appropriate selection of measuring devices.
Which factors cause the power curve to adopt a "peak"' pattern instead of the intended "plateau" pattern? The induced power profile shows that only a small part of the asphericity can be explained by laser and corneal factors; the rest should be ascribed to healing processes. The induced rates of change of axial power in the transition zone were high5: 15.0 and 45.0 D/mm in the first half of the transition zone for the 4-mm/8-mm and the 4-mm/6-mm profiles, respectively. On the rabbit corneas, significantly lower maximums of 7.5 D/mm and 9.6 D/mm were found. Healing mechanisms may smooth the high power changes in the transition zone at the expense of a smaller optical zone. The question raised is whether there is a maximum rate of change of corneal power. This hypothesis might explain the similarity in results of the two ablation profiles: high power changes would tend to stabilize around a maximum rate of change of about 10 D/mm.
The mean range of dioptric power in the 4 mm diameter central cornea was large: approximately 10 D. In normal corneas this is 2.00 (±0.50) D, in corneas after radial keratotomy, 3.80 (±2.40) D18, and after PRK for myopia, 4.20 (±1.20) D.17 Information on corneal topography in clinical trials of hyperopic PRK is scarce.12,13 From an optical point of view, the shrinking and flattening of the topographic optical zone can be considered as two different components of the regression: the first increases the aspericity, the second results in a true regression of the optical effect. With the high asphericity of these corneas it can be assumed- even without ray tracing17_that the (best corrected) quality of the retinal image would not be excellent. We conclude that the ablation profiles in the present form are not suitable for + 10 D PRK corrections in humans.
A second difference between the actual profile graphs and the induced topography is the absence of a midperipheral flat transition zone. This is surprising, since this dip in axial power is not merely a side effect of central steepening, but a conditio sine qua non for central steepening. The ring pattern of the Placido images did suggest a midperipheral flattening: the broad ring. Its localization corresponded well to expected outcomes; the mean distance from the center was 2.49 mm (expected 2.50 mm) in the 4-mm/6-mm corrected corneas, and 2.89 mm (expected 3.0 mm) in the 4-mm/8-mm corrected corneas.
Why then wasn't there a transitional flattening on the profile graphs? Two problems with topographical analysis can be discerned. First, there is a problem of spatial resolution. The transition zone in one correction is only 1 mm total width. The flattened portion is 0.5 mm, and the steepened portion is 0.5 mm, both with very rapid rates of change. With rings spaced at 0.5 mm, this cannot be detected. In addition, due to the nature of the extreme flattening, the rings in this zone are greater than 0.5 mm apart. In Figure 4, the ring is wider than the central black spot which is 0.7 mm diameter. The details of the transition zone cannot be detected if there is not a ring edge in the area. Therefore, it is not surprising that the EyeSys videokeratoscope produces an incorrect interpolation of the axial power in the transition zone. The ring pattern in the far periphery showed the unablated surface. This area was probably interpreted correctly. Thus, the topography seems to be reliable centrally up to the border of the transition zone and again in the far periphery, but interpolation in the midperiphery appears to be incorrect.
A second problem is posed by the mixed convex-concave surfaces. In two of the 4-mm/6-mm corrected corneas, the Placido image showed a double imaging of one of its rings (Fig 4). Such a double image is only possible if the surface between the two points of interest on the cornea is not continuously convex (Fig 8). The double Purkinje image is an irrefutable indication of a flat or concave area in the transition zone. This was expected from calculations of the instantaneous radius of curvature of the ablation profiles.
To the best of our knowledge, no tests have been published about the accuracy of measuring this type of mixed surface, as have been on toric19, mild aspheric convex surfaces20 and on purely concave surfaces, as the back side of rigid contact lenses. Mixed convex-concave surfaces do not have the usual corneal shape characteristics.21 If on such surfaces one or more rings have a double reflection (Fig 8), how can a topography device detect that the ninth ring is a second reflection from the eighth ring? This is a fundamental problem of the Placido-based reflection technique- not a problem of inaccurate edge detection. The problem is not solved by the instantaneous power algorithm because in the present videokeratoscopes, the results of this algorithm are limited to positive powers.
In this topographic study, a stable steepening on the cornea is possible to achieve, provided a suitable transition is present in the ablation profile. In both 4mm/8-mm and 4-mm/6-mm ablation profiles, the steepening was present in a small central zone, increasing the asphericity in the central cornea. The 4-mm/8-mm profile did not produce significantly better results than the 4-mm/6-mm ablation profile. For +10 D corrections, both ablation profiles failed to give sufficiently large zones with homogeneous refractive power. The Placido-based videokeratoscope has difficulty in measuring the changes in axial power in a very flat transition zone due to insufficient spatial resolution and mixed convex-concave surfaces.
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