- Email: [email protected]
Changes in posterior corneal curvature after photorefractive keratectomy2
Changes in posterior corneal curvature after photorefractive keratectomy Shehzad A. Naroo, MSc, W. Neil Charman, DSc ABSTRACT Purpose: To determine whether myopic ablation by excimer laser photorefractive keratectomy (PRK) affects only the anterior curvature of the cornea or whether changes also occur in the posterior corneal curvature. Setting: Department of Optometry and Neuroscience, UMIST, and Optimax Laser Eye Clinic, Manchester, United Kingdom. Methods: Sixteen patients who presented for correction of myopia in 1 eye by excimer laser PRK were followed for 3 months. Only newly presenting patients were recruited, and the untreated eyes were used as controls. The patients were examined at the initial visit (0 week) and 6 and 12 weeks post-PRK. Measurements included Orbscan topography and pachymetry, autokeratometry, and ultrasound pachymetry. Results: The mean patient age of the 8 men and 8 women was 29.6 years ⫾ 8.6 (SD) (range 20 to 47 years). The attempted mean spherical equivalent correction was between ⫺1.73 and ⫺6.43 diopters. Anterior corneal curvature and corneal thickness in the treated eyes changed systematically in relation to the amount of ablation. Posterior corneal curvature steepened in relation to the dioptric power treated. There were systematic differences between the pachymetry values obtained with the Orbscan and the ultrasound pachymeter. Conclusions: The results suggest that after myopic PRK, the thinner, ablated cornea may bulge forward slightly to steepen both anterior and posterior curvatures. This may account for the regression toward myopia that is typically found in the first few days posttreatment. The forward bulging is similar to the corneal relaxation effects observed after radial keratotomy. J Cataract Refract Surg 2000; 26:872– 878 © 2000 ASCRS and ESCRS
R
eports of corneal topography changes after excimer laser refractive surgery have increased during the
Accepted for publication December 8, 1999. From the Department of Optometry and Neuroscience, Manchester, United Kingdom. Neither author has a financial interest in any product mentioned. Russell Ambrose made the facilities of the Optimax Laser Clinic, Manchester, available and Stephen Doyle and Eamonn Hynes provided access to patients. Reprint requests to S.A. Naroo, MSc, Department of Optometry and Neuroscience, UMIST, PO Box 88, Manchester M60 1QD, United Kingdom. © 2000 ASCRS and ESCRS Published by Elsevier Science Inc.
past few years, following the widespread use of the technique to correct refractive errors. Traditionally, only changes in the curvature of the anterior corneal surface have been described, since the anterior surface is easily measured by keratometry and contributes most of the eye’s refractive power.1 Most current videokeratoscopes use Placido-disk technology, which records the dimensions of images of black-and-white concentric rings that are reflected from the anterior corneal surface. Each ring provides numerous data points, which are collated and translated into local anterior radius of curvature or power measurements. The information collected is usually presented as a contour map, with hot colors repre0886-3350/00/$–see front matter PII S0886-3350(00)00413-2
POST-PRK CHANGES IN POSTERIOR CORNEAL CURVATURE
senting steeper areas of the anterior corneal surface and cold colors representing flatter areas. Scanning slit section topography2 was recently introduced. This is similar to the earlier method of rasterstereography,3 in which real images are analyzed and not reflected images as in Placido-type topography. The Orbscan unit (Orbtek Inc.) takes 40 slit sections of the cornea during 2 scans, each lasting 0.7 seconds. Each slit section is similar to an optical section viewed through a slitlamp. The anterior and posterior corneal height profiles are reconstructed from these sections using 3dimensional ray-tracing. The method thus provides information about the anterior and posterior curvature of the cornea, as well as the corneal thickness. The curvature results are usually presented in the form of a contour map showing the height deviations from the bestfitting spheres (BFSs), but a variety of other numerical descriptions can be obtained. It has been shown that measurement of anterior surface curvature, as assessed using calibrated standards, has high validity (accuracy) and measurement of human corneal thickness, high reliability (reproducibility).4 The aim of the present study was to use the Orbscan to determine whether photorefractive keratectomy (PRK) affected only the anterior surface of the cornea or whether both anterior and posterior curvatures changed. Orbscan information about anterior and posterior curvature and corneal thickness was compared with results from standard autokeratometry and ultrasound pachymetry.
All patients were treated by 1 of 2 ophthalmologists using a Nidek EC-5000 excimer laser system. This system uses a scanning beam to correct both spherical and cylindrical refractive errors. The ablated optic zone diameter was 6.5 mm, with a blended transition zone diameter of 7.5 mm. The mean attempted spherical equivalent was ⫺3.66 diopters (D) (range ⫺1.73 to ⫺6.43 D). The mean attempted correction of initial cylindrical errors was ⫺1.04 DC (range 0.00 to –2.25 DC). Attempted corrections differed slightly from the original refractive errors because of the algorithms used, which were modified by the clinic from the original algorithm calculated by Nidek.5 The refractive status of the treated and control eyes at week 0 is shown in Table 1. The refractive error was measured by the treating surgeon. Orbscan corneal topography, Humphrey ultrasound pachymetry, and Nidek ARK 900S autokeratometry were performed on all available patients by the same clinician (S.A.N.). Orbscan corneal topography was not performed at the 6 week examination. Ultrasound pachymetry and Nidek autokeratometry were repeated 3 times at each examination and the mean values recorded. The Nidek autokeratometer assumes a value of 1.3375 for the corneal refractive index, and its design is such that the measurements refer to a zone approximately 3.3 mm in diameter; i.e., the measurements fell within the 6.5 mm diameter ablated zone in the treated eyes.
Results Patients and Methods Newly presenting patients at a local laser center were recruited sequentially. All were myopic and were presenting for refractive correction of the first eye; thus, the untreated eye could be used as a control. Measurements were made at the time of the initial visit (day of treatment, 0 week) and 6 and 12 weeks postoperatively. Sixteen patients were recruited, 8 men and 8 women. The mean age was 29.4 years ⫾ 9.4 (SD) (range 20 to 47 years). All wore contact lenses (4 rigid gaspermeable and 12 soft hydrogel) but stopped wearing them in both eyes for at least 2 weeks before the day of treatment.
Three patients did not return for follow-up examinations; 1 patient presented at 6 weeks but not at 12 weeks; 1 patient presented at 12 weeks but not at 6 weeks. All available results were included in the analysis. Table 1 shows the refractive outcome in all patients who returned after 12 weeks. Subjective dissatisfaction was not reported by any patient. Change in Anterior Corneal Power Figure 1 shows the reduction in mean Nidek autokeratometry readings between 0 and 6 weeks and 0 and 12 weeks in the treated eyes versus the treatment mean spherical equivalent (MSE). For convenience in plotting, the MSE in each control eye is the same as in the fellow treated eye.
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Table 1. Refractive corrections in the 12 patients examined at weeks 0 (pretreatment) and 12 (post-PRK). Refraction at Week 0 (Sph/Cyl)
Refraction at Week 12 (Sph/Cyl)
Patient
Treated Eye
Control Eye
Treated Eye
Control Eye
1
⫺1.50/⫺0.75
⫺1.25/⫺0.50
⫹0.25/⫺0.25
⫺1.25/⫺0.50
2
⫺2.25/⫺0.75
⫺2.00/⫺0.50
⫹0.75/⫺0.75
⫺2.00/⫺0.50
3
⫺2.25/⫺1.00
⫺2.00/⫺0.75
⫹0.50/0.00
⫺2.00/⫺0.75
4
⫺3.25/⫺0.50
⫺2.50/⫺0.50
⫹1.50/0.00
⫺2.50/⫺0.50
5
⫺3.25/⫺0.50
⫺3.75/⫺0.50
⫹0.50/0.00
⫺3.75/⫺0.50
6
⫺3.25/⫺1.50
⫺3.00/⫺1.25
⫹1.50/⫺1.00
⫺3.00/⫺1.25
7
⫺3.50/⫺1.25
⫺3.25/⫺1.00
⫺0.75/⫺0.50
8
⫺4.50/0.00
⫺3.50/0.00
⫹0.25/⫺0.50
⫺3.75/0.00
9
⫺3.75/⫺2.25
⫺3.50/⫺2.00
⫹0.25/⫺1.00
⫺3.50/⫺2.00
10
⫺4.75/⫺1.25
⫺4.00/⫺1.25
⫹0.25/⫺0.75
⫺4.00/⫺1.25
11
⫺6.25/⫺1.50
⫺1.50/0.00
⫺0.25/0.00
⫺1.50/0.00
12
⫺6.75/⫺1.25
⫺5.50/⫺0.75
⫹1.00/0.00
⫺5.75/⫺0.75
3.25/⫺1.00
Sph/Cyl ⫽ sphere/cylinder
Results in the treated eyes were similar at 6 and 12 weeks. The regression equations for the straight lines in Figure 1 are ⌬K ⫽ ⫺0.80 S ⫹ 0.45 (6 weeks) 共r2 ⫽ 0.80兲 ⌬K ⫽ ⫺0.66 S ⫹ 0.85 (12 weeks) 共r2 ⫽ 0.89兲
where ⌬K diopters is the reduction in K-value in the treated eyes and S is the intended mean spherical correction; r is the product moment correlation coefficient. A t test shows that the correlation between ⌬K and S is highly significant (P ⬍ .01) in both cases. The change in anterior corneal power in the treated eyes was roughly the same magnitude as the intended correction (i.e., the slopes of the regression equations approximate to unity), and there were only minor differences between the results at 6 and 12 weeks. There were no systematic radius changes in the untreated control eyes. The regression equation in the control eyes 12 weeks post-PRK was ⌬K ⫽ 0.05 S ⫹ 0.03 共r2 ⫽ 0.079, P ⬍ .05兲
Change in Corneal Thickness
Figure 1. (Naroo) Reduction in corneal power in the treated eyes between 0 and 6 weeks and 0 and 12 weeks measured by Nidek autokeratometry, as a function of the treatment MSE. The changes in the control eyes between 0 and 12 weeks are shown for comparison.
874
Figure 2 shows similar plots for the reduction in central corneal thickness measured by ultrasound pachymetry between 0 and 6 weeks 0 and 12 weeks in the treated eye versus the treatment MSE. The changes in corneal thickness in the control eyes between 0 and 12 weeks are shown for comparison. The corneas of the treated eyes were thinner, the reduction in thickness increasing with the magnitude of the treatment MSE. There was little change in thickness after 6 weeks.
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Figure 2. (Naroo) Reduction in central corneal thickness in the
Figure 3. (Naroo) Orbscan measurement of the change between
treated eyes between 0 and 6 weeks and 0 and 12 weeks measured by ultrasound pachymetry, as a function of the treatment MSE. Changes in the control eye between 0 and 12 weeks are shown for comparison.
0 and 12 weeks in the radius of curvature of the BFS over the central 5.0 mm corneal diameter of the anterior surface in the treated and control eyes, as a function of the treatment MSE.
The regression equations are ⌬t ⫽ ⫺15.17 S ⫹ 12.32 (6weeks) (r2 ⫽ 0.62) ⌬t ⫽ ⫺13.74 S ⫹ 19.10 (12weeks) 共r2 ⫽ 0.56兲
where ⌬t microns is the reduction in corneal thickness by ultrasound in the treated eyes and S diopters is the intended mean spherical correction. There was little difference between the results at 6 and 12 weeks. A t test showed that both correlations were significant at the P ⬍ .01 level. There were no systematic changes in the untreated control eyes. The regression equation in these eyes was ⌬t ⫽ ⫺2.99 S ⫺12.34 (12 weeks) (r2 ⫽ 0.085; P ⬎ .05, not significant) Change in Corneal Radii Measured by Orbscan Figure 3 shows the change (0 to 12 weeks) in the radius of curvature, ra, of the BFS derived for the central 5.0 mm of the 6.5 mm diameter anterior ablated zone. Figure 3 shows that the anterior surface of the treated eye flattened after PRK, whereas that of the untreated eye remained constant. This was consistent with the power results shown in Figure 1. The regression equations for the changes post-PRK in the radii of the anterior BFS as a function of the treatment MSE are
Treated ⌬ra ⫽ – 0.19 S ⫹ 0.11 (r2 ⫽ 0.87; P ⬍ .01, highly significant) Untreated ⌬ra ⫽ 0.01 S ⫺ 0.02 (r2 ⫽ 0.0067; P ⬎ .05, not significant) Figure 4 shows that there may be a decrease in posterior radius in the treated eyes. The regression equations are Treated ⌬rp⫽ 0.19 S ⫺ 0.36 (r2 ⫽ 0.31)
Figure 4. (Naroo) Orbscan measurement of the change between 0 and 12 weeks in the radius of curvature of the BFS over the central 5.0 mm corneal diameter of the posterior surface in the treated and control eyes, as a function of the treatment MSE.
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POST-PRK CHANGES IN POSTERIOR CORNEAL CURVATURE
Figure 5. (Naroo) Difference between the corneal thicknesses as measured by Orbscan and ultrasound pachymetry, as a function of treatment MSE. The lines show regression fits for the treated eyes (whose corneal thickness varied with the MSE) and the corresponding control eyes.
Untreated ⌬rp ⫽ 0.04 S ⫺ 0.20 (r2 ⫽ 0.37) The posterior steepening in the treated eyes appeared to increase with the attempted correction, although the r2 value was relatively low. In both cases, the t test suggests that the correlations were significant at about the P ⫽ .05 level. The results of Orbscan pachymetry were systematically higher than those of ultrasound pachymetry (Figure 5) by about 83.0 ⫾12.0 m.
Discussion The post-PRK changes in anterior corneal power were highly correlated with the attempted best-sphere correction. However, the magnitudes of the regression slopes were somewhat less than unity and the intercepts were greater than zero, implying that although the refractive outcome was generally satisfactory, there was not a simple 1-to-1 correlation between anterior corneal power change and the correction achieved. The changes in corneal thickness were approximately the magnitude that would be expected from the equations of Munnerlyn and coauthors,6 taking account of the preoperative MSE. The results showed little change in mean keratometry readings or ultrasound thickness between 6 and 12 weeks, suggesting that stability in the treated cornea had 876
almost been reached by 6 weeks. This agrees with numerous studies on the stabilization of postoperative refractive error. The difference between Orbscan and ultrasound pachymetry appeared to be independent of the treatment MSE, i.e., effectively the absolute value of the thickness. A similar result has been reported7,8 and may arise because of errors in the assumptions made in 1 or both methods because the noncontact Orbscan measurements include a greater thickness of tear film or, perhaps, because diffraction effects at the edge of the optical sections introduce an artifactual increase in apparent thickness. Our finding with the Orbscan of an apparent steepening in the curvature of the postoperative surface, while not perhaps surprising, is interesting. It appears that the thinner, ablated cornea may bulge forward slightly to steepen both the anterior and posterior curvatures. This would account for the regression toward myopia that is typically found in the first few postoperative days (although other factors, such as epithelial changes and edema, may also play a role). This bulging forward has obvious similarities to the corneal relaxation effects observed after radial keratotomy (RK).9 In RK, however, the more peripheral cornea is weakened, leading to peripheral steepening and central flattening, whereas in myopic PRK, the thinner and weaker central cornea results in central steepening. Steepening of the cornea’s posterior surface by a given amount has a smaller effect on the overall refraction of the eye than flattening of the anterior surface, since the index difference between the cornea and aqueous is small. For example, using the anterior and posterior radii assumed by the Gullstrand–LeGrand schematic eye (7.8 mm and 6.5 mm, respectively)10 as the starting values and corneal and aqueous indexes of 1.3771 and 1.3374, respectively, we found that a 1.0 mm increase in radius of curvature of the anterior surface decreased its convergent power by about 5.5 D. A decrease of 1.0 mm in the radius of the posterior surface, however, increased its divergent power by about 1.1 D. The combined effect of such anterior flattening and posterior steepening was to enhance the overall reduction in corneal power from the 5.5 D due to the anterior surface alone to about 6.6 D. A simple approximation to derive the change in overall corneal power for any change in the 2 radii is given in the appendix.
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At this stage, it is important to consider whether the Orbscan measurements of posterior radii can be trusted. Whereas the validity of the anterior surface measurements has been confirmed using well-calibrated test objects,4 no such confirmation of posterior surface measurements is available. In the present study, the magnitude of the Orbscan changes was what would be expected on the basis of the changes measured by autokeratometry. (Using the index assumed by the Nidek autokeratometer, a change in anterior radius of 1.0 mm from a base value of 7.8 mm would be expected to change the K-value by about 4.9 D.) Moreover, the consistency of the anterior radius measurements in the control eyes over the 12 weeks supports the reliability of these measurements. However, the instrument wrongly recorded some change in posterior radius in the control eyes, suggesting the possibility of some change in instrument calibration over the 12 weeks. At present, there is no simple method of verifying that the instrument remains correctly calibrated. We explored the short-term reliability of the Orbscan by making repeat measurements of anterior and posterior central corneal radii on the same eyes at intervals of a few days and found that the standard deviations in the BFS radius over the central 5.0 mm of cornea in an untreated eye were typically about ⫾0.041 mm for the anterior and ⫾0.035 mm for the posterior radius. In a treated eye, the standard deviations were slightly greater at ⫾0.075 mm and ⫾0.096 mm for the anterior and posterior radii, respectively. These values appear a little high compared with the finding of Lattimore and coauthors4 that the standard deviation in height measurements for a calibrated surface is only ⫾0.002 mm. However, we note that for the approximately 8.0 mm radius of the anterior cornea, an uncertainty of 0.002 mm in the sag of about 0.400 mm over a 5.0 mm diameter would give an uncertainty in radius estimate of about 0.040 mm, close to what we observed. Despite these possible instrument limitations, we think the fact that the changes in the posterior radius in the treated eyes were much greater than those in the control eyes suggests that a post-PRK steepening of the posterior surface occurs. It is possible that the posterior corneal curvature continued to change after the 12 week period of this study. More extended observations are therefore desirable. However, because little change was observed in ultrasound thickness and mean keratometry
readings after 6 weeks, we think it unlikely that posterior corneal curvature continues to change markedly after the 12 week period. Shimmura et al.11 suggest that on the basis of slitlamp, pachymetry, and Orbscan observations, posterior corneal protrusion may occur post-PRK in some cases. Wang and coauthors12 claim that similar effects may occur after laser in situ keratomileusis, although this has been disputed.13 Our observation that it occurs widely post-PRK may have implications for the safety of second procedures to correct residual refractive error. Evidently the higher the attempted correction, the thinner the residual cornea and the greater the amount of bulging and refractive regression. This in turn implies a greater need for second procedures in eyes with the thinnest postoperative corneas. Eventually, a cornea model may be derived that would be able to predict the amount of flattening of the anterior corneal surface and the amount of flexure in the posterior corneal surface for a known ablation depth in a cornea of known thickness.
References 1. Corbett MC, Rosen ES, O’Brart DPS. Corneal Topography: Principles and Applications. London, BMJ Books, 1999 2. Auffarth GU, Tetz MR, Biazid Y, Vo¨lcker HE. Measuring anterior chamber depth with the Orbscan topography system. J Cataract Refract Surg 1997; 23:1351–1355 3. Warnicki JW, Rehkopf PG, Curtin DY, et al. Corneal topography using computer analyzed rasterstereographic images. Applied Opt 1988; 27:1135–1140 4. Lattimore MR Jr, Kaupp S, Schallhorn S, Lewis R IV. Orbscan pachymetry; implications of a repeated measures and diurnal variation analysis. Ophthalmology 1999; 106:977–981 5. Chatterjee A, Shah S, Bessant DA, Doyle SJ. Results of excimer laser retreatment of residual myopia after previous photorefractive keratectomy. Ophthalmology 1997; 104:1321–1326 6. Munnerlyn CR, Koons SJ, Marshall J. Photorefractive keratectomy: a technique for laser refractive surgery. J Cataract Refract Surg 1988; 14:46 –52 7. Yaylali V, Kaufman SC, Thompson HW. Corneal thickness measurements with the Orbscan topography system and ultrasonic pachymetry. J Cataract Refract Surg 1997; 23:1345–1350 8. Liu Z, Huang AJ, Pflugfelder SC. Evaluation of corneal thickness and topography in normal eyes using the Orbscan corneal topography system. Br J Ophthalmol 1999; 83:774 –777
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9. Rand RH, Lubkin SR, Howland HC. Analytical model of corneal surgery. J Biomech Eng 1991; 113:239 –241 10. Freeman MH. Optics, 10th ed. London, Butterworths, 1999; 495 11. Shimmura S, Yang H-Y, Bissen-Miyajima H, et al. Posterior corneal protrusion after PRK. Cornea 1997; 16: 686 – 688 12. Wang Z, Chen J, Yang B. Posterior corneal surface topographic changes after laser in situ keratomileusis are related to residual corneal bed thickness. Ophthalmology 1999; 106:1999:406 – 409 13. Maloney RK. Discussion of article by Wang Z, Chen J, Yang B. Ophthalmology 1999; 106:409 – 410
Appendix Approximate Change in Corneal Power as a Function of Change in Anterior and Posterior Radii of Curvature If we assume that the cornea is thin, we can approximate its original overall refractive power, Fo, as: Fo ⫽ 共nc ⫺ 1兲/ra ⫹ 共na ⫺ nc兲/rp where ra and rp are the anterior and posterior corneal radii and nc and na are the refractive indices of the cornea and aqueous, respectively. If we change the corneal radii to ra ⫹ ⌬ra and rp ⫹ ⌬rp, the new corneal power will be Fn ⫽ 共nc ⫺ 1兲/共ra ⫹ ⌬ra兲 ⫹ 共na ⫺ nc兲/共rp ⫹ ⌬rp兲 ⫽ 共nc ⫺ 1兲/ra共1 ⫹ ⌬ra/ra兲 ⫹ 共na ⫺ nc兲/rp共1 ⫹ ⌬rp/rp兲
878
Expanding the denominators of the 2 terms and rejecting higher-order terms as being negligible if the changes in radii are small compared with the radii themselves, we can approximate Fn ⫽ 共nc ⫺ 1兲共1 ⫺ ⌬ra/ra兲/ra ⫹ 共na ⫺ nc兲共1 ⫺ ⌬rp/rp兲/rp Introducing equation (1) Fn ⫽ Fo ⫺ 共nc ⫺ 1兲⌬ra/ra2 ⫺ 共na ⫺ nc兲⌬rp/rp2 Hence the change in corneal power ⌬F ⫽ Fn ⫺ Fo ⫽ ⫺ 共nc ⫺ 1兲⌬ra/ra2 ⫺ 共na ⫺ nc兲⌬rp/rp2 Using values for the original parameters from the Gullstrand–LeGrand schematic eye10 (nc ⫽ 1.3771; na ⫽ 1.3374; ra ⫽ 7.8 mm; rp ⫽ 6.5 mm), we find that, approximately ⌬F ⫽ ⫺ 6.20⌬ra ⫹ 0.94⌬rp.......................共2兲 where the radius changes are expressed in millimeters. Note that the corneal power will be reduced by an increase in ra or a decrease in rp, but that for any magnitude of radius change the anterior surface has a greater effect. The values predicted by equation (2) for relatively large 1.0 mm radius changes differ slightly from those discussed in the text because of the approximations involved in deriving the expression.
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R
eports of corneal topography changes after excimer laser refractive surgery have increased during the
Accepted for publication December 8, 1999. From the Department of Optometry and Neuroscience, Manchester, United Kingdom. Neither author has a financial interest in any product mentioned. Russell Ambrose made the facilities of the Optimax Laser Clinic, Manchester, available and Stephen Doyle and Eamonn Hynes provided access to patients. Reprint requests to S.A. Naroo, MSc, Department of Optometry and Neuroscience, UMIST, PO Box 88, Manchester M60 1QD, United Kingdom. © 2000 ASCRS and ESCRS Published by Elsevier Science Inc.
past few years, following the widespread use of the technique to correct refractive errors. Traditionally, only changes in the curvature of the anterior corneal surface have been described, since the anterior surface is easily measured by keratometry and contributes most of the eye’s refractive power.1 Most current videokeratoscopes use Placido-disk technology, which records the dimensions of images of black-and-white concentric rings that are reflected from the anterior corneal surface. Each ring provides numerous data points, which are collated and translated into local anterior radius of curvature or power measurements. The information collected is usually presented as a contour map, with hot colors repre0886-3350/00/$–see front matter PII S0886-3350(00)00413-2
POST-PRK CHANGES IN POSTERIOR CORNEAL CURVATURE
senting steeper areas of the anterior corneal surface and cold colors representing flatter areas. Scanning slit section topography2 was recently introduced. This is similar to the earlier method of rasterstereography,3 in which real images are analyzed and not reflected images as in Placido-type topography. The Orbscan unit (Orbtek Inc.) takes 40 slit sections of the cornea during 2 scans, each lasting 0.7 seconds. Each slit section is similar to an optical section viewed through a slitlamp. The anterior and posterior corneal height profiles are reconstructed from these sections using 3dimensional ray-tracing. The method thus provides information about the anterior and posterior curvature of the cornea, as well as the corneal thickness. The curvature results are usually presented in the form of a contour map showing the height deviations from the bestfitting spheres (BFSs), but a variety of other numerical descriptions can be obtained. It has been shown that measurement of anterior surface curvature, as assessed using calibrated standards, has high validity (accuracy) and measurement of human corneal thickness, high reliability (reproducibility).4 The aim of the present study was to use the Orbscan to determine whether photorefractive keratectomy (PRK) affected only the anterior surface of the cornea or whether both anterior and posterior curvatures changed. Orbscan information about anterior and posterior curvature and corneal thickness was compared with results from standard autokeratometry and ultrasound pachymetry.
All patients were treated by 1 of 2 ophthalmologists using a Nidek EC-5000 excimer laser system. This system uses a scanning beam to correct both spherical and cylindrical refractive errors. The ablated optic zone diameter was 6.5 mm, with a blended transition zone diameter of 7.5 mm. The mean attempted spherical equivalent was ⫺3.66 diopters (D) (range ⫺1.73 to ⫺6.43 D). The mean attempted correction of initial cylindrical errors was ⫺1.04 DC (range 0.00 to –2.25 DC). Attempted corrections differed slightly from the original refractive errors because of the algorithms used, which were modified by the clinic from the original algorithm calculated by Nidek.5 The refractive status of the treated and control eyes at week 0 is shown in Table 1. The refractive error was measured by the treating surgeon. Orbscan corneal topography, Humphrey ultrasound pachymetry, and Nidek ARK 900S autokeratometry were performed on all available patients by the same clinician (S.A.N.). Orbscan corneal topography was not performed at the 6 week examination. Ultrasound pachymetry and Nidek autokeratometry were repeated 3 times at each examination and the mean values recorded. The Nidek autokeratometer assumes a value of 1.3375 for the corneal refractive index, and its design is such that the measurements refer to a zone approximately 3.3 mm in diameter; i.e., the measurements fell within the 6.5 mm diameter ablated zone in the treated eyes.
Results Patients and Methods Newly presenting patients at a local laser center were recruited sequentially. All were myopic and were presenting for refractive correction of the first eye; thus, the untreated eye could be used as a control. Measurements were made at the time of the initial visit (day of treatment, 0 week) and 6 and 12 weeks postoperatively. Sixteen patients were recruited, 8 men and 8 women. The mean age was 29.4 years ⫾ 9.4 (SD) (range 20 to 47 years). All wore contact lenses (4 rigid gaspermeable and 12 soft hydrogel) but stopped wearing them in both eyes for at least 2 weeks before the day of treatment.
Three patients did not return for follow-up examinations; 1 patient presented at 6 weeks but not at 12 weeks; 1 patient presented at 12 weeks but not at 6 weeks. All available results were included in the analysis. Table 1 shows the refractive outcome in all patients who returned after 12 weeks. Subjective dissatisfaction was not reported by any patient. Change in Anterior Corneal Power Figure 1 shows the reduction in mean Nidek autokeratometry readings between 0 and 6 weeks and 0 and 12 weeks in the treated eyes versus the treatment mean spherical equivalent (MSE). For convenience in plotting, the MSE in each control eye is the same as in the fellow treated eye.
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Table 1. Refractive corrections in the 12 patients examined at weeks 0 (pretreatment) and 12 (post-PRK). Refraction at Week 0 (Sph/Cyl)
Refraction at Week 12 (Sph/Cyl)
Patient
Treated Eye
Control Eye
Treated Eye
Control Eye
1
⫺1.50/⫺0.75
⫺1.25/⫺0.50
⫹0.25/⫺0.25
⫺1.25/⫺0.50
2
⫺2.25/⫺0.75
⫺2.00/⫺0.50
⫹0.75/⫺0.75
⫺2.00/⫺0.50
3
⫺2.25/⫺1.00
⫺2.00/⫺0.75
⫹0.50/0.00
⫺2.00/⫺0.75
4
⫺3.25/⫺0.50
⫺2.50/⫺0.50
⫹1.50/0.00
⫺2.50/⫺0.50
5
⫺3.25/⫺0.50
⫺3.75/⫺0.50
⫹0.50/0.00
⫺3.75/⫺0.50
6
⫺3.25/⫺1.50
⫺3.00/⫺1.25
⫹1.50/⫺1.00
⫺3.00/⫺1.25
7
⫺3.50/⫺1.25
⫺3.25/⫺1.00
⫺0.75/⫺0.50
8
⫺4.50/0.00
⫺3.50/0.00
⫹0.25/⫺0.50
⫺3.75/0.00
9
⫺3.75/⫺2.25
⫺3.50/⫺2.00
⫹0.25/⫺1.00
⫺3.50/⫺2.00
10
⫺4.75/⫺1.25
⫺4.00/⫺1.25
⫹0.25/⫺0.75
⫺4.00/⫺1.25
11
⫺6.25/⫺1.50
⫺1.50/0.00
⫺0.25/0.00
⫺1.50/0.00
12
⫺6.75/⫺1.25
⫺5.50/⫺0.75
⫹1.00/0.00
⫺5.75/⫺0.75
3.25/⫺1.00
Sph/Cyl ⫽ sphere/cylinder
Results in the treated eyes were similar at 6 and 12 weeks. The regression equations for the straight lines in Figure 1 are ⌬K ⫽ ⫺0.80 S ⫹ 0.45 (6 weeks) 共r2 ⫽ 0.80兲 ⌬K ⫽ ⫺0.66 S ⫹ 0.85 (12 weeks) 共r2 ⫽ 0.89兲
where ⌬K diopters is the reduction in K-value in the treated eyes and S is the intended mean spherical correction; r is the product moment correlation coefficient. A t test shows that the correlation between ⌬K and S is highly significant (P ⬍ .01) in both cases. The change in anterior corneal power in the treated eyes was roughly the same magnitude as the intended correction (i.e., the slopes of the regression equations approximate to unity), and there were only minor differences between the results at 6 and 12 weeks. There were no systematic radius changes in the untreated control eyes. The regression equation in the control eyes 12 weeks post-PRK was ⌬K ⫽ 0.05 S ⫹ 0.03 共r2 ⫽ 0.079, P ⬍ .05兲
Change in Corneal Thickness
Figure 1. (Naroo) Reduction in corneal power in the treated eyes between 0 and 6 weeks and 0 and 12 weeks measured by Nidek autokeratometry, as a function of the treatment MSE. The changes in the control eyes between 0 and 12 weeks are shown for comparison.
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Figure 2 shows similar plots for the reduction in central corneal thickness measured by ultrasound pachymetry between 0 and 6 weeks 0 and 12 weeks in the treated eye versus the treatment MSE. The changes in corneal thickness in the control eyes between 0 and 12 weeks are shown for comparison. The corneas of the treated eyes were thinner, the reduction in thickness increasing with the magnitude of the treatment MSE. There was little change in thickness after 6 weeks.
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Figure 2. (Naroo) Reduction in central corneal thickness in the
Figure 3. (Naroo) Orbscan measurement of the change between
treated eyes between 0 and 6 weeks and 0 and 12 weeks measured by ultrasound pachymetry, as a function of the treatment MSE. Changes in the control eye between 0 and 12 weeks are shown for comparison.
0 and 12 weeks in the radius of curvature of the BFS over the central 5.0 mm corneal diameter of the anterior surface in the treated and control eyes, as a function of the treatment MSE.
The regression equations are ⌬t ⫽ ⫺15.17 S ⫹ 12.32 (6weeks) (r2 ⫽ 0.62) ⌬t ⫽ ⫺13.74 S ⫹ 19.10 (12weeks) 共r2 ⫽ 0.56兲
where ⌬t microns is the reduction in corneal thickness by ultrasound in the treated eyes and S diopters is the intended mean spherical correction. There was little difference between the results at 6 and 12 weeks. A t test showed that both correlations were significant at the P ⬍ .01 level. There were no systematic changes in the untreated control eyes. The regression equation in these eyes was ⌬t ⫽ ⫺2.99 S ⫺12.34 (12 weeks) (r2 ⫽ 0.085; P ⬎ .05, not significant) Change in Corneal Radii Measured by Orbscan Figure 3 shows the change (0 to 12 weeks) in the radius of curvature, ra, of the BFS derived for the central 5.0 mm of the 6.5 mm diameter anterior ablated zone. Figure 3 shows that the anterior surface of the treated eye flattened after PRK, whereas that of the untreated eye remained constant. This was consistent with the power results shown in Figure 1. The regression equations for the changes post-PRK in the radii of the anterior BFS as a function of the treatment MSE are
Treated ⌬ra ⫽ – 0.19 S ⫹ 0.11 (r2 ⫽ 0.87; P ⬍ .01, highly significant) Untreated ⌬ra ⫽ 0.01 S ⫺ 0.02 (r2 ⫽ 0.0067; P ⬎ .05, not significant) Figure 4 shows that there may be a decrease in posterior radius in the treated eyes. The regression equations are Treated ⌬rp⫽ 0.19 S ⫺ 0.36 (r2 ⫽ 0.31)
Figure 4. (Naroo) Orbscan measurement of the change between 0 and 12 weeks in the radius of curvature of the BFS over the central 5.0 mm corneal diameter of the posterior surface in the treated and control eyes, as a function of the treatment MSE.
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Figure 5. (Naroo) Difference between the corneal thicknesses as measured by Orbscan and ultrasound pachymetry, as a function of treatment MSE. The lines show regression fits for the treated eyes (whose corneal thickness varied with the MSE) and the corresponding control eyes.
Untreated ⌬rp ⫽ 0.04 S ⫺ 0.20 (r2 ⫽ 0.37) The posterior steepening in the treated eyes appeared to increase with the attempted correction, although the r2 value was relatively low. In both cases, the t test suggests that the correlations were significant at about the P ⫽ .05 level. The results of Orbscan pachymetry were systematically higher than those of ultrasound pachymetry (Figure 5) by about 83.0 ⫾12.0 m.
Discussion The post-PRK changes in anterior corneal power were highly correlated with the attempted best-sphere correction. However, the magnitudes of the regression slopes were somewhat less than unity and the intercepts were greater than zero, implying that although the refractive outcome was generally satisfactory, there was not a simple 1-to-1 correlation between anterior corneal power change and the correction achieved. The changes in corneal thickness were approximately the magnitude that would be expected from the equations of Munnerlyn and coauthors,6 taking account of the preoperative MSE. The results showed little change in mean keratometry readings or ultrasound thickness between 6 and 12 weeks, suggesting that stability in the treated cornea had 876
almost been reached by 6 weeks. This agrees with numerous studies on the stabilization of postoperative refractive error. The difference between Orbscan and ultrasound pachymetry appeared to be independent of the treatment MSE, i.e., effectively the absolute value of the thickness. A similar result has been reported7,8 and may arise because of errors in the assumptions made in 1 or both methods because the noncontact Orbscan measurements include a greater thickness of tear film or, perhaps, because diffraction effects at the edge of the optical sections introduce an artifactual increase in apparent thickness. Our finding with the Orbscan of an apparent steepening in the curvature of the postoperative surface, while not perhaps surprising, is interesting. It appears that the thinner, ablated cornea may bulge forward slightly to steepen both the anterior and posterior curvatures. This would account for the regression toward myopia that is typically found in the first few postoperative days (although other factors, such as epithelial changes and edema, may also play a role). This bulging forward has obvious similarities to the corneal relaxation effects observed after radial keratotomy (RK).9 In RK, however, the more peripheral cornea is weakened, leading to peripheral steepening and central flattening, whereas in myopic PRK, the thinner and weaker central cornea results in central steepening. Steepening of the cornea’s posterior surface by a given amount has a smaller effect on the overall refraction of the eye than flattening of the anterior surface, since the index difference between the cornea and aqueous is small. For example, using the anterior and posterior radii assumed by the Gullstrand–LeGrand schematic eye (7.8 mm and 6.5 mm, respectively)10 as the starting values and corneal and aqueous indexes of 1.3771 and 1.3374, respectively, we found that a 1.0 mm increase in radius of curvature of the anterior surface decreased its convergent power by about 5.5 D. A decrease of 1.0 mm in the radius of the posterior surface, however, increased its divergent power by about 1.1 D. The combined effect of such anterior flattening and posterior steepening was to enhance the overall reduction in corneal power from the 5.5 D due to the anterior surface alone to about 6.6 D. A simple approximation to derive the change in overall corneal power for any change in the 2 radii is given in the appendix.
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At this stage, it is important to consider whether the Orbscan measurements of posterior radii can be trusted. Whereas the validity of the anterior surface measurements has been confirmed using well-calibrated test objects,4 no such confirmation of posterior surface measurements is available. In the present study, the magnitude of the Orbscan changes was what would be expected on the basis of the changes measured by autokeratometry. (Using the index assumed by the Nidek autokeratometer, a change in anterior radius of 1.0 mm from a base value of 7.8 mm would be expected to change the K-value by about 4.9 D.) Moreover, the consistency of the anterior radius measurements in the control eyes over the 12 weeks supports the reliability of these measurements. However, the instrument wrongly recorded some change in posterior radius in the control eyes, suggesting the possibility of some change in instrument calibration over the 12 weeks. At present, there is no simple method of verifying that the instrument remains correctly calibrated. We explored the short-term reliability of the Orbscan by making repeat measurements of anterior and posterior central corneal radii on the same eyes at intervals of a few days and found that the standard deviations in the BFS radius over the central 5.0 mm of cornea in an untreated eye were typically about ⫾0.041 mm for the anterior and ⫾0.035 mm for the posterior radius. In a treated eye, the standard deviations were slightly greater at ⫾0.075 mm and ⫾0.096 mm for the anterior and posterior radii, respectively. These values appear a little high compared with the finding of Lattimore and coauthors4 that the standard deviation in height measurements for a calibrated surface is only ⫾0.002 mm. However, we note that for the approximately 8.0 mm radius of the anterior cornea, an uncertainty of 0.002 mm in the sag of about 0.400 mm over a 5.0 mm diameter would give an uncertainty in radius estimate of about 0.040 mm, close to what we observed. Despite these possible instrument limitations, we think the fact that the changes in the posterior radius in the treated eyes were much greater than those in the control eyes suggests that a post-PRK steepening of the posterior surface occurs. It is possible that the posterior corneal curvature continued to change after the 12 week period of this study. More extended observations are therefore desirable. However, because little change was observed in ultrasound thickness and mean keratometry
readings after 6 weeks, we think it unlikely that posterior corneal curvature continues to change markedly after the 12 week period. Shimmura et al.11 suggest that on the basis of slitlamp, pachymetry, and Orbscan observations, posterior corneal protrusion may occur post-PRK in some cases. Wang and coauthors12 claim that similar effects may occur after laser in situ keratomileusis, although this has been disputed.13 Our observation that it occurs widely post-PRK may have implications for the safety of second procedures to correct residual refractive error. Evidently the higher the attempted correction, the thinner the residual cornea and the greater the amount of bulging and refractive regression. This in turn implies a greater need for second procedures in eyes with the thinnest postoperative corneas. Eventually, a cornea model may be derived that would be able to predict the amount of flattening of the anterior corneal surface and the amount of flexure in the posterior corneal surface for a known ablation depth in a cornea of known thickness.
References 1. Corbett MC, Rosen ES, O’Brart DPS. Corneal Topography: Principles and Applications. London, BMJ Books, 1999 2. Auffarth GU, Tetz MR, Biazid Y, Vo¨lcker HE. Measuring anterior chamber depth with the Orbscan topography system. J Cataract Refract Surg 1997; 23:1351–1355 3. Warnicki JW, Rehkopf PG, Curtin DY, et al. Corneal topography using computer analyzed rasterstereographic images. Applied Opt 1988; 27:1135–1140 4. Lattimore MR Jr, Kaupp S, Schallhorn S, Lewis R IV. Orbscan pachymetry; implications of a repeated measures and diurnal variation analysis. Ophthalmology 1999; 106:977–981 5. Chatterjee A, Shah S, Bessant DA, Doyle SJ. Results of excimer laser retreatment of residual myopia after previous photorefractive keratectomy. Ophthalmology 1997; 104:1321–1326 6. Munnerlyn CR, Koons SJ, Marshall J. Photorefractive keratectomy: a technique for laser refractive surgery. J Cataract Refract Surg 1988; 14:46 –52 7. Yaylali V, Kaufman SC, Thompson HW. Corneal thickness measurements with the Orbscan topography system and ultrasonic pachymetry. J Cataract Refract Surg 1997; 23:1345–1350 8. Liu Z, Huang AJ, Pflugfelder SC. Evaluation of corneal thickness and topography in normal eyes using the Orbscan corneal topography system. Br J Ophthalmol 1999; 83:774 –777
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9. Rand RH, Lubkin SR, Howland HC. Analytical model of corneal surgery. J Biomech Eng 1991; 113:239 –241 10. Freeman MH. Optics, 10th ed. London, Butterworths, 1999; 495 11. Shimmura S, Yang H-Y, Bissen-Miyajima H, et al. Posterior corneal protrusion after PRK. Cornea 1997; 16: 686 – 688 12. Wang Z, Chen J, Yang B. Posterior corneal surface topographic changes after laser in situ keratomileusis are related to residual corneal bed thickness. Ophthalmology 1999; 106:1999:406 – 409 13. Maloney RK. Discussion of article by Wang Z, Chen J, Yang B. Ophthalmology 1999; 106:409 – 410
Appendix Approximate Change in Corneal Power as a Function of Change in Anterior and Posterior Radii of Curvature If we assume that the cornea is thin, we can approximate its original overall refractive power, Fo, as: Fo ⫽ 共nc ⫺ 1兲/ra ⫹ 共na ⫺ nc兲/rp where ra and rp are the anterior and posterior corneal radii and nc and na are the refractive indices of the cornea and aqueous, respectively. If we change the corneal radii to ra ⫹ ⌬ra and rp ⫹ ⌬rp, the new corneal power will be Fn ⫽ 共nc ⫺ 1兲/共ra ⫹ ⌬ra兲 ⫹ 共na ⫺ nc兲/共rp ⫹ ⌬rp兲 ⫽ 共nc ⫺ 1兲/ra共1 ⫹ ⌬ra/ra兲 ⫹ 共na ⫺ nc兲/rp共1 ⫹ ⌬rp/rp兲
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Expanding the denominators of the 2 terms and rejecting higher-order terms as being negligible if the changes in radii are small compared with the radii themselves, we can approximate Fn ⫽ 共nc ⫺ 1兲共1 ⫺ ⌬ra/ra兲/ra ⫹ 共na ⫺ nc兲共1 ⫺ ⌬rp/rp兲/rp Introducing equation (1) Fn ⫽ Fo ⫺ 共nc ⫺ 1兲⌬ra/ra2 ⫺ 共na ⫺ nc兲⌬rp/rp2 Hence the change in corneal power ⌬F ⫽ Fn ⫺ Fo ⫽ ⫺ 共nc ⫺ 1兲⌬ra/ra2 ⫺ 共na ⫺ nc兲⌬rp/rp2 Using values for the original parameters from the Gullstrand–LeGrand schematic eye10 (nc ⫽ 1.3771; na ⫽ 1.3374; ra ⫽ 7.8 mm; rp ⫽ 6.5 mm), we find that, approximately ⌬F ⫽ ⫺ 6.20⌬ra ⫹ 0.94⌬rp.......................共2兲 where the radius changes are expressed in millimeters. Note that the corneal power will be reduced by an increase in ra or a decrease in rp, but that for any magnitude of radius change the anterior surface has a greater effect. The values predicted by equation (2) for relatively large 1.0 mm radius changes differ slightly from those discussed in the text because of the approximations involved in deriving the expression.
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