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Corneal asphericity after hyperopic laser in situ keratomileusis
Corneal asphericity after hyperopic laser in situ keratomileusis Chun Chen Chen, MD, Alexander Izadshenas, MD, M. Ali Asghar Rana, MD, Dimitri T. Azar, MD Purpose: To analyze corneal asphericity after hyperopic laser in situ keratomileusis (LASIK) and its relationship to the clinical outcomes. Setting: Corneal and Refractive Surgery Service, Massachusetts Eye and Ear Infirmary, Boston, Massachusetts, USA. Methods: In a retrospective case series, 23 patients (33 eyes) with hyperopia or hyperopic astigmatism who had LASIK were evaluated. A computer program (Holladay Diagnostic Summary, EyeSys Laboratories) was used to analyze corneal asphericity (Q) before and after LASIK. Corneal asphericity was evaluated to determine the association with the postoperative refractive error, best spectaclecorrected visual acuity (BSCVA), uncorrected visual acuity (UCVA), achieved refractive correction, mean corneal power (K), refractive yield (achieved/attempted correction), and keratometric yield (change in keratometry/attempted correction). Results: After hyperopic LASIK, all corneas exhibited increased negative central Q. The postoperative corneal radius of curvature, BSCVA, and refractive and keratometric yields were not significantly correlated with the preoperative Q values. The asphericity change, ⌬Q, was highly correlated with the achieved correction (r ⫽ 0.747, P ⬍ .0001). The postoperative Q value correlated well with the preoperative value (r ⫽ 0.534, P ⬍ .05) and the achieved correction (r ⫽ 0.601, P ⬍ .05) but not with the ⌬Q. Neither the postoperative Q nor the ⌬Q was correlated with the spherical equivalent, K, BSCVA, or UCVA. Conclusions: Asphericity may be a useful quantitative descriptor of the corneal optical contour after hyperopic LASIK. Negative central Q increased after hyperopic LASIK, especially when greater degrees of refractive correction were attempted. J Cataract Refract Surg 2002; 28:1539 –1545 © 2002 ASCRS and ESCRS
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ver the past 2 decades, photorefractive keratectomy (PRK) and laser in situ keratomileusis (LASIK) have emerged as effective procedures for the surgical correction of myopia and hyperopia.1 The basic algorithms have been provided by Missotten and coauthors2 and Munnerlyn and coauthors.3 To correct hyperopia and hyperopic astigmatism, the central cornea should be steepened. The ablation profile for hyperopic Accepted for publication May 6, 2002. Reprint requests to Dimitri T. Azar, Corneal, External Disease and Refractive Surgery Service, Massachusetts Eye and Ear Infirmary, 243 Charles Street, Boston, Massachusetts 02114, USA. E-mail: [email protected]. © 2002 ASCRS and ESCRS Published by Elsevier Science Inc.
correction requires a smooth transition zone to prevent an abrupt step at the peripheral edge (Figure 1).4 Corneal curvature can be described by a point-bypoint array of corneal radius or by mathematical models to approximate the corneal contour. The corneal asphericity (Q) in the conic equation has been widely applied to describe the corneal surface.5–7 Most human corneas flatten from the center to the periphery and are prolate (negative asphericity; Q ⬍ 0). Some corneas steepen from the center to the periphery and are oblate (positive asphericity; Q ⬎ 0).5–10 In unoperated eyes, the Q ranges from 0.50 to ⫺0.88.6,7,11,12 The shape of the corneal surface has a major affect on the eye’s optical performance. Based on topographic 0886-3350/02/$–see front matter PII S0886-3350(02)01541-9
CORNEAL ASPHERICITY AFTER HYPEROPIC LASIK
Figure 1. (Chen) Diagrams of Q after hyperopic LASIK. The laser profile of hyperopic ablation comprises an optical zone (5.0 mm) and a smooth transition zone (9.0 mm). The central 0.5 mm is untreated by the laser. For the same apical curvature, (2) is more prolate than (3).
observations, the cornea exhibits a positive central asphericity after myopic PRK, changing from a prolate (negative asphericity) to an oblate optical contour.5,10 –14 Using a mathematical model, Gatinel and coauthors15 have demonstrated that the postoperative theoretical Q can be accurately approximated by a bestfit conic section and that in oblate corneas, myopic treatments result in more oblate configurations within the treatment area, which is consistent with the clinical observations. In prolate corneas, however, they observed a discrepancy between the clinically reported oblateness after myopic LASIK and the theoretical prediction of increased prolateness.15 They hypothesized that this discrepancy may be related to myopic laser nomograms, low accuracy of topographic measurements, and wound healing (epithelial hyperplasia and/or stromal remodeling).15 The effect of hyperopic LASIK on corneal asphericity remains to be elucidated. This is important because altering the corneal shape may affect the visual outcome after surgery. In this study, we analyzed the outcomes and topographic changes in hyperopic and hyperopic astigmatic patients after LASIK using a quantitative descriptor of Q. We also investigated the relationship of postoperative Q to preoperative Q, corneal curvature, and clinical outcomes including mean keratometric power, best spectacle-corrected visual acuity (BSCVA), and achieved and attempted correction. We believe this is the first report of Q and asphericity changes (⌬Q) after hyperopic LASIK.
Patients and Methods Laser in situ keratomileusis was performed in 23 patients (33 eyes) with hyperopia (with or without astigmatism), and the preoperative and postoperative visual outcomes and Q were compared. All patients had preoperative and postopera1540
tive (1, 3, and/or 6 months) evaluations and Q measurements including uncorrected visual acuity (UCVA), BSCVA, Q, spherical equivalent refraction (SE), corneal power (K), and radius of curvature (R). Patients were treated by a single surgeon (D.T.A.) with the VISX Star S2 laser using an optical zone of 5.0 mm and a peripheral zone of 9.0 mm. Patient age (at the initial LASIK surgery), sex, and preoperative UCVA, BSCVA, Q value, SE, K, and R values were tabulated and analyzed.
Corneal Asphericity Measurements and Calculations of Refractive Outcomes Profile distortion maps were derived from standard computer-assisted videokeratographic data (EyeSys, Premier Laser Systems). The EyeSys index of Q is derived from the axial R data collected within the central 4.5 mm diameter region for a given cornea and is based on assumptions developed by the literature reporting derivation of Q through conic-section analysis.16,17 The mean keratometric measurements were obtained from computerized videokeratography. Snellen visual acuity was converted to decimal acuity; logMAR acuity was obtained by taking the negative log value of the decimal acuity. To determine whether the initial Q influences the predictability of the hyperopic treatment, the effect of the preoperative Q on the refractive yield (defined as the achieved/attempted correction) and the keratometric yield (defined as the change in keratometry/attempted correction) was evaluated.
Statistical Analysis Data were entered into a computer spreadsheet (Excel 7.0, Microsoft) and imported into statistical software (Statview, SAS Institute). Depending on the amount of astigmatic refractive error, eyes were divided into 2 groups. The inclusion criterion for Group A was “spherical” hyperopia with cylinder less than ⫺0.5 diopter (D). (The spherical hyperopia was treated with astigmatic correction.) The inclusion criterion for Group B was hyperopia with cylinder more than ⫺0.5 D. (The hyperopic or mixed astigmatism was treated in addition to the spherical hyperopic components.) Statistical analyses were performed using the MannWhitney U test for analyses of age, sex, mean follow-up, preoperative Q, K, R, SE, and preoperative logMAR of UCVA and BSCVA between the 2 groups. The postoperative data obtained at the 1-month (n ⫽ 33 eyes), 3-month (n ⫽ 22 eyes), and 6-month (n ⫽ 15 eyes) examinations were compared with the preoperative data. The data obtained in months 1 to 6 were averaged and used for statistical analyses. The Wilcoxon signed rank test was used to compare preoperative and postoperative data including Q and ⌬Q. The associations between Q and the clinical outcomes were tested using Spearman rank correlation and regression analysis. Analysis of BSCVA and UCVA between subgroups of achieved correction and Q was performed using the Kruskal-
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Table 1. Demographic data. Characteristic Number of eyes Gender (F/M) Age (y)* Retreatment
Group A
Group B
21
12
14/7
4/8
54.05 ⫾ 8.72 (31–71)
57.42 ⫾ 8.13 (36–66)
4
1
*Mean ⫾ SD (range)
Wallis test. A P value less than 0.05 was considered statistically significant.
Results Demographic and preoperative refractive data are summarized in Table 1. The mean follow-up was 22.90 weeks ⫾ 19.35 (SD) (Group A) and 23.17 ⫾ 19.62 weeks (Group B). There were no statistically significant differences between the 2 groups in age, duration of follow-up, and preoperative Q, K, UCVA, and BSCVA. The visual outcomes and comparisons of preoperative and postoperative refractive data are shown in Table 2. In Group A, there was a statistically significant increase in the mean negative Q at 1 month (– 0.97 ⫾ 0.39) and 3 months (– 0.82 ⫾ 0.43) (P ⬍ .05). In Group B, similar increases in the mean negative asphericity were seen at 1 month (– 0.72 ⫾ 0.70) and 6 months (–1.24 ⫾ 0.88) (P ⬍ .05). The SE was reduced in all patients after treatment (P ⬍ .0001). Statistically significant improvement in the mean UCVA (logMAR) was seen at 1 month in Group A (0.20 ⫾ 0.17) and Group B (– 0.20 ⫾ 0.15) (P ⬍ .0001). The mean UCVA in both groups at 3 months (Group A, 0.22 ⫾
0.32; Group B, 0.19 ⫾ 0.08) and 6 months (Group A, 0.26 ⫾ 0.18; Group B, 0.16 ⫾ 0.08) was not statistically different from that at 1 month. The mean postoperative BSCVA (logMAR) was not significantly different from the preoperative data in Group A (1 month, 0.04 ⫾ 0.09; 3 months, 0.04 ⫾ 0.14; 6 months, 0.06 ⫾ 0.13) and Group B (1 month, 0.04 ⫾ 0.06, 3 months, 0.01 ⫾ 0.09; 6 months, 0.03 ⫾ 0.05). The mean K value increased after treatment. The increase was statistically significant at 1 month (44.79 ⫾ 1.20), 3 months (44.64 ⫾ 1.13), and 6 months (45.77 ⫾ 1.62) in Group A (P ⫽ .0002); it was not significant in Group B (43.0 ⫾ 2.78, 44.12 ⫾ 0.01, 45.02 ⫾ 2.12, respectively). Influence of Preoperative Asphericity on Refractive Outcomes The preoperative Q was not associated with the postoperative R, BSCVA, or UCVA at 1, 3, and 6 months. There was also no correlation between the preoperative Q and the refractive or keratometric yield during the follow-up (Figure 2). Factors Influencing Postoperative Asphericity The postoperative Q correlated well with the preoperative Q in Groups A and B (r ⫽ 0.56, P ⫽ .01; r ⫽ 0.57, P ⫽ .02, respectively). The ⌬Q did not correlate with the preoperative Q. There was also no correlation between the postoperative Q and the preoperative corneal curvature (K or R); postoperative SE, K, UCVA; or BSCVA. There was a linear correlation between the achieved correction and the postoperative Q (Group A, r ⫽ 0.57, P ⬍ .05; Group B, r ⫽ 0.67, P ⬍ .05) (Figure 3) and also between the attempted correction and the
Table 2. Preoperative and postoperative data 1 month after LASIK. Group A Parameter
Preoperative
Postoperative*
Group B P Value
Preoperative
Postoperative*
P Value ⬍.0001
UCVA (logMAR)
0.51 ⫾ 0.33
0.20 ⫾ 0.17
⬍.0001
0.52 ⫾ 0.22
⫺0.20 ⫾ 0.15
BSCVA (logMAR)
0.01 ⫾ 0.09
0.04 ⫾ 0.09
NS
0.03 ⫾ 0.05
0.04 ⫾ 0.06
NS
SE
2.40 ⫾ 1.21
⫺0.37 ⫾ 0.58
⬍.0001
0.99 ⫾ 1.98
0.12 ⫾ 0.66
⬍.0001
K
43.12 ⫾ 1.13
44.79 ⫾ 1.20
⬍.05
43.10 ⫾ 1.29
43.00 ⫾ 2.78
⬍.05
Q
⫺0.32 ⫾ 0.20
⫺0.97 ⫾ 0.39
⬍.05
⫺0.43 ⫾ 0.49
⫺0.72 ⫾ 0.70
⬍.05
NS ⫽ not significant; UCVA ⫽ uncorrected visual acuity; BSCVA ⫽ best spectacle-corrected visual acuity; SE ⫽ spherical equivalent; K ⫽ central keratometry; Q ⫽ asphericity All values are mean ⫾ SD. *At 1-month examination
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Figure 3. (Chen) Correlation between the postoperative Q and the achieved correction in Groups A (F) and B (Œ). The correlation coefficient (r) in Group A was 0.57 (P ⫽ .01) and in Group B, 0.67 (P ⫽ .02).
Figure 2. (Chen) Influence of preoperative Q on predictability in Groups A (F) and B (Œ). A: Poor correlation between preoperative Q (Preop Q) and refractive yield (%) is noted. The refractive yield is a ratio of achieved over attempted correction. The correlation coefficient (r) in Group A was 0.14 (P ⫽ .54) and in Group B, 0.14 (P ⫽ .68). B: Similarly, poor correlation is noted between Preop Q and the keratometric yield. The keratometric yield is the ratio of keratometric change over attempted correction. The correlation coefficient (r) in Group A was 0.33 (P ⫽ .14) and in Group B, 0.04 (P ⫽ .92).
postoperative Q (Group A, r ⫽ 0.53, P ⬍ .05; Group B, r ⫽ 0.71, P ⬍ .05). Subdividing the data into 2 subgroups according to preoperative asphericity (0 ⬎ Q0 ⬎ ⫺0.19, ⫺0.2 ⬎ Q0 ⬎ ⫺2.0) showed a trend of increased postoperative prolateness with increased preoperative prolateness for the same magnitude of treatment (Figure 4). Factors Influencing Asphericity Change After Hyperopic LASIK In Groups A and B, the correlation between achieved or attempted correction and the ⌬Q was highly 1542
significant (r ⫽ 0.73, P ⬍ .0001; r ⫽ 0.75, P ⬍ .0001, respectively) (Figure 5). The ⌬Q was associated with corneal keratometric change (⌬K) in Group A (r ⫽ 0.67, P ⬍ .05) but not in Group B. The correlations of UCVA, BSCVA, SE, K, Q, ⌬R (corneal radius change), ⌬UCVA (UCVA change), and ⌬BCVA (BSCVA change) with ⌬Q were not statistically significant. The correlation between ⌬K, ⌬R, achieved correction, attempted correction, ⌬UCVA, and ⌬BSCVA was examined. The achieved correction was highly correlated with the attempted correction in Groups A and B (r ⫽ 0.90, P ⬍ .0001; r ⫽ 0.95, P ⬍ .0001, respectively). The correlation between ⌬K and the achieved correction was significant in Group A (r ⫽ 0.78, P ⬍ .05) but not in Group B. The ratio of refractive change versus keratometric change (achieved correction/⌬K) was 1.47 ⫾ 0.33 (Group A) and 1.12 ⫾ 1.66 (Group B). There was no correlation between ⌬K, ⌬R, ⌬BSCVA, ⌬UCVA, and ⌬Q. Influence of Postoperative Asphericity and of Achieved Correction on PostoperativeVisual Acuity Since the postoperative Q may be influenced by the degree of attempted correction, the patients were divided into 4 subgroups: I, high negative postoperative Q value (⬍ ⫺0.8) and high achieved correction (⬎2.5 D); II, low negative postoperative Q value (ⱖ ⫺0.8) and high achieved correction (⬎2.5 D); III, high negative postoperative Q value (⬍ ⫺0.8) and low achieved correction (ⱕ2.5 D); and IV, low negative postoperative Q value (ⱖ ⫺0.8) and low achieved correction (ⱕ 2.5 D) (Table 3). The postoperative BSCVA and UCVA did
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Figure 4. (Chen) Influence of preoperative Q on postoperative Q and magnitudes of achieved correction. Subgroup I: Preop Q ⬎ ⫺0.2 (F). Subgroup II: Preop Q ⬍ ⫺0.2 (Œ). In corneas initially more prolate (subgroup I), postoperative prolateness increased for the same magnitude of treatment.
not differ significantly among the subgroups. There were no significant differences in ⌬BSCVA in the 4 subgroups (Table 3).
Discussion Our data suggest that the more prolate the cornea preoperatively, the more prolate it will be after hyperopic LASIK using the VISX laser. Additionally, the ⌬Q and the postoperative Q correlated well with the attempted and achieved corrections. Other factors that we could not analyze in this study may also influence the postoperative Q after hyperopic LASIK; these include the laser algorithm, wound healing, and flap rearrangement over the treatment bed. In hyperopic and hyperopic astigmatic ablation, the ablation profile includes a central optical zone and a peripheral transition zone. A preliminary requirement for an effective transition zone is that the profile is smooth.4 An abrupt step would cause compensatory healing responses, resulting in regression of the implemented correction. We used a central optical zone of 5.0 mm and a peripheral transition zone of 9.0 mm in hyperopic and hyperopic astigmatic treatment. Although central steepening is accompanied by a predetermined amount of midperipheral flattening during hyperopic PRK,4 the laser homogeneity, applied fluence, location of the laser ablation, differential masking of the incoming laser by the effluent plume, and laser
Figure 5. (Chen) Linear regression of ⌬Q and achieved correction in Groups A (F) and B (Œ). The correlation coefficient (r) in Group A was 0.73 (P ⫽ .0002) and in Group B, 0.75 (P ⫽ .005).
tissue interaction will further influence the ablation profile and the final postoperative Q. The wound-healing process and flap rearrangement are thought to compensate for part of the tissue loss after laser ablation. Studies of rabbit cornea wound healing after hyperopic PRK by Dierick and coauthors18 show a lenticular stromal regrowth of about 50% of the ablated tissue. Stromal thickening in the optical zone and epithelial thickening of about 20% in the midtransition zone resulted in increased corneal asphericity. This process may be similar to the epithelial thickening that occurs after myopic LASIK in human corneas.19 The healing response of epithelial hyperplasia and stromal remodeling may modify the specific effect induced by the hyperopic ablation and could contribute to the increased prolateness after hyperopic LASIK. This is consistent with our findings that ⌬Q was related to corrections but not to preoperative or postoperative Q, corneal curvature, SE, and visual acuity. Negative Q may influence visual performance directly by lowering spherical aberrations, although this finding has not been definitively demonstrated.12 Kiely and coauthors7 show that the theoretical Q value for completely eliminating the Seidel spherical aberrations is ⫺0.528, which implies that the untreated cornea corrects approximately half the eye’s spherical aberrations.20 Accordingly, the spherical aberrations may be further reduced after hyperopic treatment because of aspheric curvature change. In our study, however, no
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Table 3. Visual acuity in the 4 subgroups. Postoperative Q*
Achieved Correction*
BSCVA† (logMAR)
UCVA† (logMAR)
⌬BSCVA† (logMAR)
I (n ⫽ 12)
High
High
0.07 ⫾ 0.12
0.21 ⫾ 0.19
0.03 ⫾ 0.07
II (n ⫽ 5)
Low
High
0.00 ⫾ 0.04
0.18 ⫾ 0.07
0.03 ⫾ 0.05
Subgroup
III (n ⫽ 4)
High
Low
0.04 ⫾ 0.04
0.11 ⫾ 0.09
0.02 ⫾ 0.07
IV (n ⫽ 13)
Low
Low
0.01 ⫾ 0.04
0.16 ⫾ 0.15
⫺0.001 ⫾ 0.05
BSCVA ⫽ best spectacle-corrected visual acuity; UCVA ⫽ uncorrected visual acuity; ⌬BSCVA ⫽ change in BSCVA *High postoperative asphericity, ⬍ ⫺ 0.80; low postoperative asphericity, ⱖ ⫺ 0.80; high correction, ⬎ 2.5 D; low correction, ⱕ 2.5 D † Mean ⫾ SD
direct correlation was found between increased prolateness and improved BSCVA and UCVA. Sheridan and Douthwaite21 found no significant difference in Q among patients with emmetropia, myopia, or hyperopia. Carney and coauthors22 observe that the corneal Q value becomes more positive as the level of myopia increases; the corneal Q value in eyes with high myopia (⬎4.0 D) was significantly more positive than in those with emmetropia or low myopia. Recently, Budak et al.20 demonstrated that the Q values were less negative in eyes with moderate myopia (⫺2.0 to 6.0 D) than in those with hyperopia (ⱖ1.0 D). In our series, there was no overall correlation between the Q value and the SE refraction before or after treatment. The precision and accuracy of corneal topography systems in measuring Q may be less than that of measuring the apical R.9,23 Douthwaite23 used calibrated convex ellipsoidal surfaces of known apical radius and asphericity to assess the accuracy of the EyeSys videokeratoscope. Theoretically, this device appeared to overestimate both Q and R when the corneal surface approached sphere shape. In our study, the Q after refractive surgery may have also been influenced by the treatment centration and pupil size. Additional limitations of the current study include its retrospective nature, the unavailability of near visual acuity and longterm follow-up data, and the relatively small number of patients. Nevertheless, several conclusions can be drawn from this study: (1) Prolate corneas show increased prolateness after hyperopic LASIK. (2) The increase was highly correlated with the attempted and achieved corrections. (3) The increased prolateness did not correlate with visual or refractive outcomes. We did not treat 1544
oblate corneas, so our conclusions may be valid for hyperopic treatment of prolate corneas only.
References 1. Zadok D, Maskaleris G, Montes M, et al. Hyperopic laser in situ keratomileusis with the Nidek EC-500 excimer laser. Ophthalmology 2000; 107:1132–1137 2. Missotten L, Boving R, Franc¸ois G, Coutteel C. Experimental excimer laser keratomileusis. Bull Soc Belge Ophtalmol 1986; 220:103–120 3. Munnerlyn CR, Koons SJ, Marshall J. Photorefractive keratectomy: a technique for laser refractive surgery. J Cataract Refract Surg 1988; 14:46 –52 4. Dierick HG, Missotten L. Corneal ablation profiles for correction of hyperopia with the excimer laser. J Refract Surg 1996; 12:767–773 5. Hersh PS, Shah SI, Holladay JT. Corneal asphericity following excimer laser photorefractive keratectomy; Summit PRK Topography Study Group. Ophthalmic Surg Lasers 1996; 27(suppl):S421–S428 6. Mandell RB, St. Helen R. Mathematical model of the corneal contour. Br J Physiol Opt 1971; 26:183–197 7. Kiely PM, Smith G, Carney LG. The mean shape of the human cornea. Opt Acta 1982; 8:1027–1040 8. Eghbali F, Yeung KK, Maloney RK. Topographic determination of corneal asphericity and its lack of effect on the refractive outcome of radial keratotomy. Am J Ophthalmol 1995; 119:275–280 9. Douthwaite WA, Hough T, Edwards K, Notay H. The EyeSys videokeratoscopic assessment of apical radius and p-value in the normal human cornea. Ophthalmic Physiol Opt 1999; 19:467–474 10. Hersh PS, Schwartz-Goldstein BH. Corneal topography of phase III excimer laser photorefractive keratectomy; characterization and clinical effects: the Summit Photorefractive Keratectomy Topography Study Group. Ophthalmology 1995; 102:963–978 11. Maguire LJ, Zabel RW, Parker P, Lindstrom RL. Topography and raytracing analysis of patients with excellent visual acuity 3 months after excimer laser photorefractive
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12.
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keratectomy for myopia. Refract Corneal Surg 1991; 7:122–128 Seiler T, Reckmann W, Maloney RK. Effective spherical aberration of the cornea as a quantitative descriptor in corneal topography. J Cataract Refract Surg 1993; 19: 155–165 Trocme´ SD, Mack KA, Gill KS, et al. Corneal topography after excimer laser photorefractive keratectomy for myopia. J Am Optom Assoc 1997; 68:448 –451 Holladay JT, Dudeja DR, Chang J. Functional vision and corneal changes after laser in situ keratomileusis determined by contrast sensitivity, glare testing, and corneal topography. J Cataract Refract Surg 1999; 25:663–669 Gatinel D, Hoang-Xuan T, Azar DT. Determination of corneal asphericity after myopia surgery with the excimer laser: a mathematical model. Invest Ophthalmol Vis Sci 2001; 42:1736 –1742 Holladay JT. Corneal topography using the Holladay Diagnostic Summary. J Cataract Refract Surg 1997; 23: 209 –221 Holmes-Higgin DK, Burris TE. Corneal surface topography and associated visual performance with INTACS for myopia; phase III clinical trial results; the INTACS Study Group. Ophthalmology 2000; 107:2061–2071 Dierick HG, Van Mellaert CE, Missotten L. Histology of rabbit corneas after 10-diopter photorefractive keratectomy for hyperopia. J Refract Surg 1999; 15:459 –468
19. Spadea L, Fasciani R, Necozione S, Balestrazzi E. Role of the corneal epithelium in refractive changes following laser in situ keratomileusis for high myopia. J Refract Surg 2000; 16:133–139 20. Budak K, Khater TT, Friedman NJ, et al. Evaluation of relationships among refractive and topographic parameters. J Cataract Refract Surg 1999; 25:814 –820 21. Sheridan M, Douthwaite WA. Corneal asphericity and refractive error. Ophthalmic Physiol Opt 1989; 9:235– 238 22. Carney LG, Mainstone JC, Henderson BA. Corneal topography and myopia; a cross-sectional study. Invest Ophthalmol Vis Sci 1997; 38:311–320 23. Douthwaite WA. EyeSys corneal topography measurement applied to calibrated ellipsoidal convex surfaces. Br J Ophthalmol 1995; 79:797–801 From the Corneal and Refractive Surgery Service, Massachusetts Eye and Ear Infirmary, the Schepens Eye Research Institute, and Harvard Medical School, Boston, Massachusetts, USA. Supported by the New England Corneal Transplant Research Fund, Massachusetts Lions Eye Research Fund, Boston, Massachusetts, USA, and Research to Prevent Blindness Lew R. Wasserman Merit Award (Azar). None of the authors has a financial interest in any product mentioned.
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O
ver the past 2 decades, photorefractive keratectomy (PRK) and laser in situ keratomileusis (LASIK) have emerged as effective procedures for the surgical correction of myopia and hyperopia.1 The basic algorithms have been provided by Missotten and coauthors2 and Munnerlyn and coauthors.3 To correct hyperopia and hyperopic astigmatism, the central cornea should be steepened. The ablation profile for hyperopic Accepted for publication May 6, 2002. Reprint requests to Dimitri T. Azar, Corneal, External Disease and Refractive Surgery Service, Massachusetts Eye and Ear Infirmary, 243 Charles Street, Boston, Massachusetts 02114, USA. E-mail: [email protected]. © 2002 ASCRS and ESCRS Published by Elsevier Science Inc.
correction requires a smooth transition zone to prevent an abrupt step at the peripheral edge (Figure 1).4 Corneal curvature can be described by a point-bypoint array of corneal radius or by mathematical models to approximate the corneal contour. The corneal asphericity (Q) in the conic equation has been widely applied to describe the corneal surface.5–7 Most human corneas flatten from the center to the periphery and are prolate (negative asphericity; Q ⬍ 0). Some corneas steepen from the center to the periphery and are oblate (positive asphericity; Q ⬎ 0).5–10 In unoperated eyes, the Q ranges from 0.50 to ⫺0.88.6,7,11,12 The shape of the corneal surface has a major affect on the eye’s optical performance. Based on topographic 0886-3350/02/$–see front matter PII S0886-3350(02)01541-9
CORNEAL ASPHERICITY AFTER HYPEROPIC LASIK
Figure 1. (Chen) Diagrams of Q after hyperopic LASIK. The laser profile of hyperopic ablation comprises an optical zone (5.0 mm) and a smooth transition zone (9.0 mm). The central 0.5 mm is untreated by the laser. For the same apical curvature, (2) is more prolate than (3).
observations, the cornea exhibits a positive central asphericity after myopic PRK, changing from a prolate (negative asphericity) to an oblate optical contour.5,10 –14 Using a mathematical model, Gatinel and coauthors15 have demonstrated that the postoperative theoretical Q can be accurately approximated by a bestfit conic section and that in oblate corneas, myopic treatments result in more oblate configurations within the treatment area, which is consistent with the clinical observations. In prolate corneas, however, they observed a discrepancy between the clinically reported oblateness after myopic LASIK and the theoretical prediction of increased prolateness.15 They hypothesized that this discrepancy may be related to myopic laser nomograms, low accuracy of topographic measurements, and wound healing (epithelial hyperplasia and/or stromal remodeling).15 The effect of hyperopic LASIK on corneal asphericity remains to be elucidated. This is important because altering the corneal shape may affect the visual outcome after surgery. In this study, we analyzed the outcomes and topographic changes in hyperopic and hyperopic astigmatic patients after LASIK using a quantitative descriptor of Q. We also investigated the relationship of postoperative Q to preoperative Q, corneal curvature, and clinical outcomes including mean keratometric power, best spectacle-corrected visual acuity (BSCVA), and achieved and attempted correction. We believe this is the first report of Q and asphericity changes (⌬Q) after hyperopic LASIK.
Patients and Methods Laser in situ keratomileusis was performed in 23 patients (33 eyes) with hyperopia (with or without astigmatism), and the preoperative and postoperative visual outcomes and Q were compared. All patients had preoperative and postopera1540
tive (1, 3, and/or 6 months) evaluations and Q measurements including uncorrected visual acuity (UCVA), BSCVA, Q, spherical equivalent refraction (SE), corneal power (K), and radius of curvature (R). Patients were treated by a single surgeon (D.T.A.) with the VISX Star S2 laser using an optical zone of 5.0 mm and a peripheral zone of 9.0 mm. Patient age (at the initial LASIK surgery), sex, and preoperative UCVA, BSCVA, Q value, SE, K, and R values were tabulated and analyzed.
Corneal Asphericity Measurements and Calculations of Refractive Outcomes Profile distortion maps were derived from standard computer-assisted videokeratographic data (EyeSys, Premier Laser Systems). The EyeSys index of Q is derived from the axial R data collected within the central 4.5 mm diameter region for a given cornea and is based on assumptions developed by the literature reporting derivation of Q through conic-section analysis.16,17 The mean keratometric measurements were obtained from computerized videokeratography. Snellen visual acuity was converted to decimal acuity; logMAR acuity was obtained by taking the negative log value of the decimal acuity. To determine whether the initial Q influences the predictability of the hyperopic treatment, the effect of the preoperative Q on the refractive yield (defined as the achieved/attempted correction) and the keratometric yield (defined as the change in keratometry/attempted correction) was evaluated.
Statistical Analysis Data were entered into a computer spreadsheet (Excel 7.0, Microsoft) and imported into statistical software (Statview, SAS Institute). Depending on the amount of astigmatic refractive error, eyes were divided into 2 groups. The inclusion criterion for Group A was “spherical” hyperopia with cylinder less than ⫺0.5 diopter (D). (The spherical hyperopia was treated with astigmatic correction.) The inclusion criterion for Group B was hyperopia with cylinder more than ⫺0.5 D. (The hyperopic or mixed astigmatism was treated in addition to the spherical hyperopic components.) Statistical analyses were performed using the MannWhitney U test for analyses of age, sex, mean follow-up, preoperative Q, K, R, SE, and preoperative logMAR of UCVA and BSCVA between the 2 groups. The postoperative data obtained at the 1-month (n ⫽ 33 eyes), 3-month (n ⫽ 22 eyes), and 6-month (n ⫽ 15 eyes) examinations were compared with the preoperative data. The data obtained in months 1 to 6 were averaged and used for statistical analyses. The Wilcoxon signed rank test was used to compare preoperative and postoperative data including Q and ⌬Q. The associations between Q and the clinical outcomes were tested using Spearman rank correlation and regression analysis. Analysis of BSCVA and UCVA between subgroups of achieved correction and Q was performed using the Kruskal-
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Table 1. Demographic data. Characteristic Number of eyes Gender (F/M) Age (y)* Retreatment
Group A
Group B
21
12
14/7
4/8
54.05 ⫾ 8.72 (31–71)
57.42 ⫾ 8.13 (36–66)
4
1
*Mean ⫾ SD (range)
Wallis test. A P value less than 0.05 was considered statistically significant.
Results Demographic and preoperative refractive data are summarized in Table 1. The mean follow-up was 22.90 weeks ⫾ 19.35 (SD) (Group A) and 23.17 ⫾ 19.62 weeks (Group B). There were no statistically significant differences between the 2 groups in age, duration of follow-up, and preoperative Q, K, UCVA, and BSCVA. The visual outcomes and comparisons of preoperative and postoperative refractive data are shown in Table 2. In Group A, there was a statistically significant increase in the mean negative Q at 1 month (– 0.97 ⫾ 0.39) and 3 months (– 0.82 ⫾ 0.43) (P ⬍ .05). In Group B, similar increases in the mean negative asphericity were seen at 1 month (– 0.72 ⫾ 0.70) and 6 months (–1.24 ⫾ 0.88) (P ⬍ .05). The SE was reduced in all patients after treatment (P ⬍ .0001). Statistically significant improvement in the mean UCVA (logMAR) was seen at 1 month in Group A (0.20 ⫾ 0.17) and Group B (– 0.20 ⫾ 0.15) (P ⬍ .0001). The mean UCVA in both groups at 3 months (Group A, 0.22 ⫾
0.32; Group B, 0.19 ⫾ 0.08) and 6 months (Group A, 0.26 ⫾ 0.18; Group B, 0.16 ⫾ 0.08) was not statistically different from that at 1 month. The mean postoperative BSCVA (logMAR) was not significantly different from the preoperative data in Group A (1 month, 0.04 ⫾ 0.09; 3 months, 0.04 ⫾ 0.14; 6 months, 0.06 ⫾ 0.13) and Group B (1 month, 0.04 ⫾ 0.06, 3 months, 0.01 ⫾ 0.09; 6 months, 0.03 ⫾ 0.05). The mean K value increased after treatment. The increase was statistically significant at 1 month (44.79 ⫾ 1.20), 3 months (44.64 ⫾ 1.13), and 6 months (45.77 ⫾ 1.62) in Group A (P ⫽ .0002); it was not significant in Group B (43.0 ⫾ 2.78, 44.12 ⫾ 0.01, 45.02 ⫾ 2.12, respectively). Influence of Preoperative Asphericity on Refractive Outcomes The preoperative Q was not associated with the postoperative R, BSCVA, or UCVA at 1, 3, and 6 months. There was also no correlation between the preoperative Q and the refractive or keratometric yield during the follow-up (Figure 2). Factors Influencing Postoperative Asphericity The postoperative Q correlated well with the preoperative Q in Groups A and B (r ⫽ 0.56, P ⫽ .01; r ⫽ 0.57, P ⫽ .02, respectively). The ⌬Q did not correlate with the preoperative Q. There was also no correlation between the postoperative Q and the preoperative corneal curvature (K or R); postoperative SE, K, UCVA; or BSCVA. There was a linear correlation between the achieved correction and the postoperative Q (Group A, r ⫽ 0.57, P ⬍ .05; Group B, r ⫽ 0.67, P ⬍ .05) (Figure 3) and also between the attempted correction and the
Table 2. Preoperative and postoperative data 1 month after LASIK. Group A Parameter
Preoperative
Postoperative*
Group B P Value
Preoperative
Postoperative*
P Value ⬍.0001
UCVA (logMAR)
0.51 ⫾ 0.33
0.20 ⫾ 0.17
⬍.0001
0.52 ⫾ 0.22
⫺0.20 ⫾ 0.15
BSCVA (logMAR)
0.01 ⫾ 0.09
0.04 ⫾ 0.09
NS
0.03 ⫾ 0.05
0.04 ⫾ 0.06
NS
SE
2.40 ⫾ 1.21
⫺0.37 ⫾ 0.58
⬍.0001
0.99 ⫾ 1.98
0.12 ⫾ 0.66
⬍.0001
K
43.12 ⫾ 1.13
44.79 ⫾ 1.20
⬍.05
43.10 ⫾ 1.29
43.00 ⫾ 2.78
⬍.05
Q
⫺0.32 ⫾ 0.20
⫺0.97 ⫾ 0.39
⬍.05
⫺0.43 ⫾ 0.49
⫺0.72 ⫾ 0.70
⬍.05
NS ⫽ not significant; UCVA ⫽ uncorrected visual acuity; BSCVA ⫽ best spectacle-corrected visual acuity; SE ⫽ spherical equivalent; K ⫽ central keratometry; Q ⫽ asphericity All values are mean ⫾ SD. *At 1-month examination
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Figure 3. (Chen) Correlation between the postoperative Q and the achieved correction in Groups A (F) and B (Œ). The correlation coefficient (r) in Group A was 0.57 (P ⫽ .01) and in Group B, 0.67 (P ⫽ .02).
Figure 2. (Chen) Influence of preoperative Q on predictability in Groups A (F) and B (Œ). A: Poor correlation between preoperative Q (Preop Q) and refractive yield (%) is noted. The refractive yield is a ratio of achieved over attempted correction. The correlation coefficient (r) in Group A was 0.14 (P ⫽ .54) and in Group B, 0.14 (P ⫽ .68). B: Similarly, poor correlation is noted between Preop Q and the keratometric yield. The keratometric yield is the ratio of keratometric change over attempted correction. The correlation coefficient (r) in Group A was 0.33 (P ⫽ .14) and in Group B, 0.04 (P ⫽ .92).
postoperative Q (Group A, r ⫽ 0.53, P ⬍ .05; Group B, r ⫽ 0.71, P ⬍ .05). Subdividing the data into 2 subgroups according to preoperative asphericity (0 ⬎ Q0 ⬎ ⫺0.19, ⫺0.2 ⬎ Q0 ⬎ ⫺2.0) showed a trend of increased postoperative prolateness with increased preoperative prolateness for the same magnitude of treatment (Figure 4). Factors Influencing Asphericity Change After Hyperopic LASIK In Groups A and B, the correlation between achieved or attempted correction and the ⌬Q was highly 1542
significant (r ⫽ 0.73, P ⬍ .0001; r ⫽ 0.75, P ⬍ .0001, respectively) (Figure 5). The ⌬Q was associated with corneal keratometric change (⌬K) in Group A (r ⫽ 0.67, P ⬍ .05) but not in Group B. The correlations of UCVA, BSCVA, SE, K, Q, ⌬R (corneal radius change), ⌬UCVA (UCVA change), and ⌬BCVA (BSCVA change) with ⌬Q were not statistically significant. The correlation between ⌬K, ⌬R, achieved correction, attempted correction, ⌬UCVA, and ⌬BSCVA was examined. The achieved correction was highly correlated with the attempted correction in Groups A and B (r ⫽ 0.90, P ⬍ .0001; r ⫽ 0.95, P ⬍ .0001, respectively). The correlation between ⌬K and the achieved correction was significant in Group A (r ⫽ 0.78, P ⬍ .05) but not in Group B. The ratio of refractive change versus keratometric change (achieved correction/⌬K) was 1.47 ⫾ 0.33 (Group A) and 1.12 ⫾ 1.66 (Group B). There was no correlation between ⌬K, ⌬R, ⌬BSCVA, ⌬UCVA, and ⌬Q. Influence of Postoperative Asphericity and of Achieved Correction on PostoperativeVisual Acuity Since the postoperative Q may be influenced by the degree of attempted correction, the patients were divided into 4 subgroups: I, high negative postoperative Q value (⬍ ⫺0.8) and high achieved correction (⬎2.5 D); II, low negative postoperative Q value (ⱖ ⫺0.8) and high achieved correction (⬎2.5 D); III, high negative postoperative Q value (⬍ ⫺0.8) and low achieved correction (ⱕ2.5 D); and IV, low negative postoperative Q value (ⱖ ⫺0.8) and low achieved correction (ⱕ 2.5 D) (Table 3). The postoperative BSCVA and UCVA did
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Figure 4. (Chen) Influence of preoperative Q on postoperative Q and magnitudes of achieved correction. Subgroup I: Preop Q ⬎ ⫺0.2 (F). Subgroup II: Preop Q ⬍ ⫺0.2 (Œ). In corneas initially more prolate (subgroup I), postoperative prolateness increased for the same magnitude of treatment.
not differ significantly among the subgroups. There were no significant differences in ⌬BSCVA in the 4 subgroups (Table 3).
Discussion Our data suggest that the more prolate the cornea preoperatively, the more prolate it will be after hyperopic LASIK using the VISX laser. Additionally, the ⌬Q and the postoperative Q correlated well with the attempted and achieved corrections. Other factors that we could not analyze in this study may also influence the postoperative Q after hyperopic LASIK; these include the laser algorithm, wound healing, and flap rearrangement over the treatment bed. In hyperopic and hyperopic astigmatic ablation, the ablation profile includes a central optical zone and a peripheral transition zone. A preliminary requirement for an effective transition zone is that the profile is smooth.4 An abrupt step would cause compensatory healing responses, resulting in regression of the implemented correction. We used a central optical zone of 5.0 mm and a peripheral transition zone of 9.0 mm in hyperopic and hyperopic astigmatic treatment. Although central steepening is accompanied by a predetermined amount of midperipheral flattening during hyperopic PRK,4 the laser homogeneity, applied fluence, location of the laser ablation, differential masking of the incoming laser by the effluent plume, and laser
Figure 5. (Chen) Linear regression of ⌬Q and achieved correction in Groups A (F) and B (Œ). The correlation coefficient (r) in Group A was 0.73 (P ⫽ .0002) and in Group B, 0.75 (P ⫽ .005).
tissue interaction will further influence the ablation profile and the final postoperative Q. The wound-healing process and flap rearrangement are thought to compensate for part of the tissue loss after laser ablation. Studies of rabbit cornea wound healing after hyperopic PRK by Dierick and coauthors18 show a lenticular stromal regrowth of about 50% of the ablated tissue. Stromal thickening in the optical zone and epithelial thickening of about 20% in the midtransition zone resulted in increased corneal asphericity. This process may be similar to the epithelial thickening that occurs after myopic LASIK in human corneas.19 The healing response of epithelial hyperplasia and stromal remodeling may modify the specific effect induced by the hyperopic ablation and could contribute to the increased prolateness after hyperopic LASIK. This is consistent with our findings that ⌬Q was related to corrections but not to preoperative or postoperative Q, corneal curvature, SE, and visual acuity. Negative Q may influence visual performance directly by lowering spherical aberrations, although this finding has not been definitively demonstrated.12 Kiely and coauthors7 show that the theoretical Q value for completely eliminating the Seidel spherical aberrations is ⫺0.528, which implies that the untreated cornea corrects approximately half the eye’s spherical aberrations.20 Accordingly, the spherical aberrations may be further reduced after hyperopic treatment because of aspheric curvature change. In our study, however, no
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Table 3. Visual acuity in the 4 subgroups. Postoperative Q*
Achieved Correction*
BSCVA† (logMAR)
UCVA† (logMAR)
⌬BSCVA† (logMAR)
I (n ⫽ 12)
High
High
0.07 ⫾ 0.12
0.21 ⫾ 0.19
0.03 ⫾ 0.07
II (n ⫽ 5)
Low
High
0.00 ⫾ 0.04
0.18 ⫾ 0.07
0.03 ⫾ 0.05
Subgroup
III (n ⫽ 4)
High
Low
0.04 ⫾ 0.04
0.11 ⫾ 0.09
0.02 ⫾ 0.07
IV (n ⫽ 13)
Low
Low
0.01 ⫾ 0.04
0.16 ⫾ 0.15
⫺0.001 ⫾ 0.05
BSCVA ⫽ best spectacle-corrected visual acuity; UCVA ⫽ uncorrected visual acuity; ⌬BSCVA ⫽ change in BSCVA *High postoperative asphericity, ⬍ ⫺ 0.80; low postoperative asphericity, ⱖ ⫺ 0.80; high correction, ⬎ 2.5 D; low correction, ⱕ 2.5 D † Mean ⫾ SD
direct correlation was found between increased prolateness and improved BSCVA and UCVA. Sheridan and Douthwaite21 found no significant difference in Q among patients with emmetropia, myopia, or hyperopia. Carney and coauthors22 observe that the corneal Q value becomes more positive as the level of myopia increases; the corneal Q value in eyes with high myopia (⬎4.0 D) was significantly more positive than in those with emmetropia or low myopia. Recently, Budak et al.20 demonstrated that the Q values were less negative in eyes with moderate myopia (⫺2.0 to 6.0 D) than in those with hyperopia (ⱖ1.0 D). In our series, there was no overall correlation between the Q value and the SE refraction before or after treatment. The precision and accuracy of corneal topography systems in measuring Q may be less than that of measuring the apical R.9,23 Douthwaite23 used calibrated convex ellipsoidal surfaces of known apical radius and asphericity to assess the accuracy of the EyeSys videokeratoscope. Theoretically, this device appeared to overestimate both Q and R when the corneal surface approached sphere shape. In our study, the Q after refractive surgery may have also been influenced by the treatment centration and pupil size. Additional limitations of the current study include its retrospective nature, the unavailability of near visual acuity and longterm follow-up data, and the relatively small number of patients. Nevertheless, several conclusions can be drawn from this study: (1) Prolate corneas show increased prolateness after hyperopic LASIK. (2) The increase was highly correlated with the attempted and achieved corrections. (3) The increased prolateness did not correlate with visual or refractive outcomes. We did not treat 1544
oblate corneas, so our conclusions may be valid for hyperopic treatment of prolate corneas only.
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19. Spadea L, Fasciani R, Necozione S, Balestrazzi E. Role of the corneal epithelium in refractive changes following laser in situ keratomileusis for high myopia. J Refract Surg 2000; 16:133–139 20. Budak K, Khater TT, Friedman NJ, et al. Evaluation of relationships among refractive and topographic parameters. J Cataract Refract Surg 1999; 25:814 –820 21. Sheridan M, Douthwaite WA. Corneal asphericity and refractive error. Ophthalmic Physiol Opt 1989; 9:235– 238 22. Carney LG, Mainstone JC, Henderson BA. Corneal topography and myopia; a cross-sectional study. Invest Ophthalmol Vis Sci 1997; 38:311–320 23. Douthwaite WA. EyeSys corneal topography measurement applied to calibrated ellipsoidal convex surfaces. Br J Ophthalmol 1995; 79:797–801 From the Corneal and Refractive Surgery Service, Massachusetts Eye and Ear Infirmary, the Schepens Eye Research Institute, and Harvard Medical School, Boston, Massachusetts, USA. Supported by the New England Corneal Transplant Research Fund, Massachusetts Lions Eye Research Fund, Boston, Massachusetts, USA, and Research to Prevent Blindness Lew R. Wasserman Merit Award (Azar). None of the authors has a financial interest in any product mentioned.
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