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The Effect of Corneal Wavefront Aberrations on Corneal Pseudoaccommodation
The Effect of Corneal Wavefront Aberrations on Corneal Pseudoaccommodation ELIZABETH YEU, LI WANG, AND DOUGLAS D. KOCH ● PURPOSE:
To determine the effect on corneal pseudoaccommodation of anterior corneal wavefront aberrations in normal corneas and corneas with prior myopic or hyperopic photorefractive keratectomy (PRK) or laserassisted in situ keratomileusis (LASIK). ● DESIGN: Theoretical study. ● METHODS: In 220 normal eyes, 102 myopic-PRK eyes, and 106 hyperopic-LASIK/PRK eyes, anterior corneal higher-order aberrations (HOAs, third to sixth order, 6and 4-mm pupils) were computed from the Atlas corneal elevation data using the VOL-CT program. Using the ZernikeTool, corneal optical image quality was evaluated by the polychromatic modulation transfer function with Stiles-Crawford effect. Defocus from ⴚ3.0 diopters (D) to ⴙ3.0 D was added to corneal HOAs, and depth of focus was defined as the ranges over which the polychromatic modulation transfer function maintains 80% of the peak value (DOF80) and 50% of the peak value (DOF50). The depth of focus values between groups were compared, stepwise multiple regression was used to assess if any Zernike terms significantly contributed to the depth of focus, and correlation analysis was performed to evaluate the correlation between depth of focus and corneal HOAs. ● RESULTS: The depth of focus varied widely between corneas, especially in corneas with prior hyperopicLASIK/PRK. For 6-mm pupil, mean depth of focus values in myopic-PRK and hyperopic-LASIK/PRK corneas were significantly greater than those for normal corneas, and for 4-mm pupil, depth of focus values in hyperopic-LASIK/PRK corneas were greater than those in normal and myopic-PRK corneas. Zernike terms significantly contributing to both DOF80 and DOF50 were fourth- and sixth-order spherical aberration and fourth- and sixth-order astigmatism in normal corneas, third-order vertical coma and fourth-order tetrafoil in myopic-PRK corneas, and third-order vertical coma and fourth-order astigmatism in hyperopic-LASIK/ PRK corneas. Depth of focus had weak to moderate positive correlation with HOAs (Pearson correlation coefficient r ranged from 0.300 to 0.583). Accepted for publication Oct 17, 2011. From the Cullen Eye Institute, Department of Ophthalmology, Baylor College of Medicine, Houston, Texas. Inquiries to Elizabeth Yeu, Department of Ophthalmology, Baylor College of Medicine, 6565 Fannin, NC205, Houston, TX 77030; e-mail: [email protected]
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● CONCLUSION:
These theoretical calculations suggest that certain corneal wavefront aberrations affect corneal pseudoaccommodation. To predict corneal pseudoaccommodation, the most important Zernike term is spherical aberration in normal eyes and coma in eyes with prior laser corneal surgery. (Am J Ophthalmol 2012;153: 972–981. © 2012 by Elsevier Inc. All rights reserved.)
F
OLLOWING CATARACT SURGERY WITH IMPLANTA-
tion of a monofocal intraocular lens (IOL), some patients attain surprisingly good uncorrected near and distance vision. This phenomenon is referred to as apparent accommodation1 or pseudoaccommodation. Studies have shown that the pseudoaccommodation is inversely proportional to the pupillary diameter and positively correlated with the depth of field and corneal multifocality.2– 4 Oshika and associates assessed in pseudophakic eyes the relationship between apparent accommodation and wavefront aberrations of the cornea.5 They found that the root mean square values of the total third-order (coma-like) aberrations of the cornea were significantly correlated to the apparent accommodation. Evidence for the cornea’s role in pseudoaccommodation has also been noted in eyes that have undergone myopic corneal refractive surgery, with treated patients demonstrating enhanced distancecorrected near acuity and greater measured accommodative range.6,7 Pseudoaccommodation has been traditionally studied using subjective measurements. The purpose of this theoretical study was to assess potential corneal pseudoaccommodation as expressed by calculated depth of focus values and to correlate specific higher-order aberrations (HOAs) to the corneal depth of focus values that were calculated from the corneas of eyes in the cataract population, as well as in eyes following myopic and hyperopic excimer laser ablation.
PATIENTS AND METHODS ● PATIENTS: We included data from 3 groups of patients who visited our clinic or underwent myopic or hyperopic photorefractive keratectomy (PRK) or laser-assisted in situ keratomileusis (LASIK) between May 2002 and March 2007. The first group included 220 eyes of 137 patients, aged 40 to 80 years, with no prior corneal surgery. These subjects were selected from our preoperative cataract
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0002-9394/$36.00 doi:10.1016/j.ajo.2011.10.019
FIGURE 1. Corneal wavefront aberrations in normal, myopicPRK, and hyperopic-LASIK/PRK corneas for 6-mm pupil (Top) and 4-mm pupil (Bottom) (*: significant difference between myopic-PRK corneas and normal cornea; ⽥: significant difference between hyperopic-LASIK/PRK corneas and normal cornea, all P < .05 with Bonferroni correction). PRK ⴝ photorefractive keratectomy; LASIK ⴝlaser-assisted in situ keratomileusis.
patients, and their corneas were measured before undergoing cataract surgery. The second group had 102 eyes of 77 patients, aged 22 to 45 years, who underwent wavefrontguided myopic-PRK by 1 surgeon using the CustomVue STAR laser system (Abbott Medical Optics Inc [AMO], Santa Ana, California, USA) and who had 6 months of follow-up. Lastly, the third group included 106 eyes of 80 patients aged 40 to 59 years who underwent standard (81 eyes) or wavefront-guided (7 eyes) hyperopic-LASIK or wavefront-guided hyperopic-PRK (18 eyes) by 1 surgeon using the AMO STAR laser system. Minimum follow-up was 3 months for LASIK eyes and 6 months for PRK eyes. Inclusion criteria included: 1) no corneal pathology; 2) no prior contact lens wear or wear discontinued 4 weeks for rigid gas permeable lens, 3 weeks for toric soft contact lenses, and 2 weeks for soft contact lenses; and 3) Humphrey Atlas corneal topographic maps with no missing data points within the central 7-mm zone (Carl Zeiss Inc, Pleasanton, California, USA). VOL. 153, NO. 5
FIGURE 2. Box plot of corneal pseudoaccommodation depth of focus (DOF) values for 6-mm pupil (Top) and 4-mm pupil (Bottom). DOF80 ⴝ depth of focus maintaining polychromatic modulation transfer >80% of peak value; DOF50 ⴝ depth of focus maintaining polychromatic modulation transfer >50% of peak value; PRK ⴝ photorefractive keratectomy; LASIK ⴝ laser-assisted in situ keratomileusis.
In the myopic and hyperopic groups, we included corneas with different procedures. In our clinic, during that period of time, wavefront-guided myopic-PRK was the dominant procedure for myopic corneal laser surgery. Because of the later approval of the wavefront-guided LASIK for hyperopia by the Food and Drug Administration, the majority of the eyes in the hyperopic group had undergone conventional hyperopic LASIK. ● DEPTH OF FOCUS ON THE CORNEA:
Corneal wavefront aberrations up to sixth order for 6- and 4-mm pupils were computed from Humphrey Atlas corneal elevation data using the VOL-CT program (Sarver and Associates Inc, Carbondale, Illinois, USA), which uses the standards for calculation and reporting the optical aberrations of eyes as proposed by Thibos and associates.8 The topographic maps were recentered around the entrance pupil, and wavefront aberrations
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FIGURE 3. Percentage of eyes with certain amount of corneal pseudoaccommodation depth of focus evaluated by DOF80 (Top left) and DOF50 (Top right) for 6-mm pupil and DOF80 (Bottom left) and DOF50 (Bottom right) for 4-mm pupil. DOF80 ⴝ depth of focus maintaining polychromatic modulation transfer >80% of peak value; DOF50 ⴝ depth of focus maintaining polychromatic modulation transfer >50% of peak value; PRK ⴝ photorefractive keratectomy; LASIK ⴝ laser-assisted in situ keratomileusis.
from the cornea were calculated using a corneal refractive index of 1.376 for the wavelength of 555 nm. Corneal optical image quality was evaluated by the polychromatic modulation transfer function with StilesCrawford effect. The polychromatic modulation transfer function was calculated using the ZernikeTool program (Abbott Medical Optics Inc).9 With this program, 7 wavelengths (400, 450, 500, 550, 600, 650, and 700 nm) were used to represent the visible spectrum, and the polychromatic point spread function with Stiles-Crawford effect was weighted in the imaging plane based on the retinal spectral response function. To evaluate the effect of defocus on corneal image quality, defocus from ⫺3.0 diopters (D) to ⫹3.0 D in 0.1-D intervals was added to the HOAs of the corneas. Desired defocus in diopter was converted to wavefront coefficient in m and added to the second-order defocus term using the following equation derived from the method described by Applegate and associates:10 974
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C02 ⫽
SR2 ⫺ 4兹3
where C20 is the Zernike coefficient in m for the second-order defocus term, S is the dioptric power of the sphere expressed in diopter, and R is the radius of the pupil expressed in mm. The polychromatic modulation transfer function at 15 cycles/degree (equivalent to visual acuity of 20/40 object) was used, and depth of focus was defined by 2 criteria based on the polychromatic modulation transfer function at 15 cycles/degree: 1) the range over which the polychromatic modulation transfer function maintains 80% of the peak value (DOF80);11 and 2) the range over which the polychromatic modulation transfer function maintains 50% of the peak value (DOF50)12 (this criterion represents a 50% drop in image quality, which could still provide adequate near acuity). OF
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TABLE 1. Corneal Pseudoaccommodation Depth of Focus Values in Each Group (Mean ⫾ SD, [range]) 6-mm Pupil Group
Normal corneas (n ⫽ 220) Myopic-PRK corneas (n ⫽ 102) Hyperopic-LASIK/PRK corneas (n ⫽ 106)
4-mm Pupil
DOF80 (D)
DOF50 (D)
DOF80 (D)
DOF50 (D)
0.53 ⫾ 0.08 (0.4 to 0.8) 0.57 ⫾ 0.13a (0.4 to 1.3) 0.61 ⫾ 0.20a (0.3 to 1.4)
0.96 ⫾ 0.15 (0.6 to 1.7) 1.04 ⫾ 0.25b (0.6 to 2.4) 1.18 ⫾ 0.43b (0.6 to 2.7)
0.55 ⫾ 0.14c (0.4 to 1.4) 0.55 ⫾ 0.15c (0.3 to 1.4) 0.63 ⫾ 0.22 (0.4 to 1.5)
1.03 ⫾ 0.34d (0.7 to 2.6) 1.05 ⫾ 0.40d (0.6 to 2.9) 1.27 ⫾ 0.51 (0.7 to 3.5)
D ⫽ diopters; DOF50 ⫽ depth of focus maintaining polychromatic modulation transfer ⱖ50% of peak value; DOF80 ⫽ depth of focus maintaining polychromatic modulation transfer ⱖ80% of peak value; LASIK ⫽ laser-assisted in situ keratomileusis; PRK ⫽ photorefractive keratectomy. a,b,c,d For each criterion, depths of focus between groups were significantly different except for pair with a,b,c,d (all P ⬍ .05 with Bonferroni correction).
TABLE 2. Corneal Wavefront Zernike Terms Significantly Contributing to the Corneal Pseudoaccommodation Depth of Focus Values for 6-mm Pupil Group
Normal corneas Myopic-PRK corneas Hyperopic-LASIK/PRK corneas
Criterion
Multiple Correlation Coefficient R
Zernike Terms in Descending Order of Importance
DOF80 DOF50 DOF80 DOF50 DOF80 DOF50
0.530 0.547 0.521 0.401 0.469 0.561
Z(6,0), Z(4,0), Z(6,2), Z(4,⫺4), Z(4,2), and Z(5,⫺5) Z(4,0), Z(4,2), Z(6,0), Z(3,⫺1), Z(3,⫺3), and Z(6,2) Z(5,1), Z(3,1), Z(3,⫺1), and Z(4,4) Z(3,⫺1), Z(4,4), and Z(3,3) Z(3,1), Z(3,⫺1), and Z(4,2) Z(4,2), Z(5,⫺3), Z(4,0), Z(3,⫺1), Z(5,3), and Z(6,⫺4)
DOF50 ⫽ depth of focus maintaining polychromatic modulation transfer ⱖ50% of peak value; DOF80 ⫽ depth of focus maintaining polychromatic modulation transfer ⱖ80% of peak value; LASIK ⫽ laser-assisted in situ keratomileusis; PRK ⫽ photorefractive keratectomy.
● STATISTICAL ANALYSIS: The depth of focus values between groups were compared using Mann-Whitney test. Correlation analysis was performed to evaluate the correlation between depth of focus and root mean square (RMS) values of total higher-order aberrations (HOAs, third to sixth order) and third-order, fourth-order, fifthorder, and sixth-order wavefront aberrations of the cornea. Stepwise multiple regression was used to assess if any Zernike terms significantly contributed to the depth of focus. For this purpose, for the left eyes, Zernike coefficients for these Zernike terms with mirror symmetry between both eyes were flipped to match the right eye.13 SPSS 15.0 for Windows (SPSS Inc, Chicago, Illinois, USA) was used for statistical analysis. The Bonferroni correction was employed for multiple tests. A probability of less than 5% (P ⬍ .05) was considered statistically significant.
RESULTS ● CORNEAL ZERNIKE COEFFICIENTS:
Figure 1 shows the corneal HOAs in normal, myopic-PRK, and hyperopicLASIK/PRK corneas. Compared to normal corneas, for a 6-mm pupil, myopic-PRK and hyperopic-LASIK/PRK cor-
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neas each had significantly different mean coefficient values for 6 Zernike terms: Z(3,⫺3), Z(3,3), Z(4,⫺4), Z(4,0), Z(5,1), and Z(6,0) for myopia and Z(3,⫺3), Z(3,1), Z(3,3), Z(4,0), Z(4,4), and Z(5,1) for hyperopia (Figure 1, Top). For a 4-mm pupil, compared to normal corneas, ablated corneas had significantly different mean coefficient values for 2 Zernike terms: Z(3,⫺3) and Z(6,0) for myopicPRK corneas and Z(3,⫺3) and Z(4,0) for hyperopicLASIK/PRK corneas (Figure 1, Bottom) (all P ⬍ .05 with Bonferroni correction). ● DEPTH OF FOCUS VALUES:
The depth of focus varied widely among corneas, especially in corneas with prior hyperopic-LASIK/PRK (Figure 2). The distributions of the depth of focus values are shown in Figure 3. Table 1 shows the depth of focus values in each group. There were no significant differences in mean depth of focus values between the 6-mm pupil and 4-mm pupil within each group of eyes. The mean DOF80 and DOF50 values for myopic-PRK corneas were greater than those for normal corneas by 0.04 D and 0.08 D for the 6-mm pupil (both P ⬍ .05 with Bonferroni correction) and by 0.00 D and 0.02 D for the 4-mm pupil, respectively (both P ⬎ .05 with Bonferroni correction). The mean DOF80 and
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TABLE 3. Pearson Correlation Coefficient Values Between Corneal Pseudoaccommodation Depth of Focus Values and Corneal Wavefront Root Mean Square Values RMS Values
Normal corneas 6-mm pupil DOF80 DOF50 4-mm pupil DOF80 DOF50 Myopic-PRK corneas 6-mm pupil DOF80 DOF50 4-mm pupil DOF80 DOF50 Hyperopic-LASIK/PRK corneas 6-mm pupil DOF80 DOF50 4-mm pupil DOF80 DOF50
HOAs RMS
Third-order RMS
Fourth-order RMS
Fifth-order RMS
Sixth-order RMS
0.303a 0.382a
0.227a 0.257a
0.221a 0.326a
0.164 0.261a
0.200 0.224a
0.345a 0.478a
0.323a 0.379a
0.198 0.311a
0.230a 0.439a
0.188 0.326a
0.300a 0.211
0.240 0.203
0.221 0.101
0.248 0.259
0.121 0.137
0.255 0.324a
0.230 0.382a
0.239 0.126
0.128 0.065
0.003 0.043
0.461a 0.583a
0.468a 0.570a
0.228 0.333a
0.073 0.171
0.146 0.230
0.040 ⫺0.016
0.172 0.080
0.026 ⫺0.020
⫺0.020 ⫺0.069
0.014 0.004
DOF50 ⫽ depth of focus maintaining polychromatic modulation transfer ⱖ50% of peak value; DOF80 ⫽ depth of focus maintaining polychromatic modulation transfer ⱖ80% of peak value; HOAs ⫽ higher-order aberrations; LASIK ⫽ laser-assisted in situ keratomileusis; PRK ⫽ photorefractive keratectomy; RMS ⫽ root mean square. a Significant correlation (P ⬍ .05 with Bonferroni correction).
DOF50 values for hyperopic LASIK/PRK corneas were greater than those for normal corneas by 0.08 D and 0.22 D for the 6-mm pupil (both P ⬍ .05 with Bonferroni correction) and by 0.08 D and 0.24 D for the 4-mm pupil respectively (both P ⬍ .05 with Bonferroni correction). Lastly, the mean DOF80 and DOF50 values for hyperopic LASIK/PRK corneas were greater than those for myopicPRK corneas by 0.04 D and 0.14 D for the 6-mm pupil (both P ⬎ .05 with Bonferroni correction) and by 0.08 D and 0.22 D for the 4-mm pupil (both P ⬍ .05 with Bonferroni correction). Although not demonstrated in Table 1, in the hyperopic-LASIK/PRK group, there were no differences between depth of focus values among corneas that underwent prior standard LASIK, wavefrontguided LASIK, or wavefront-guided PRK (all P ⬎ .05 with Bonferroni correction).
spherical aberration (Z(4,0)) and astigmatism (Z(4,2)) and sixth-order spherical aberration (Z(6,0)) and astigmatism (Z(6,2)) were significant contributors to both DOF80 and DOF50. The regression formulas for predicting the depth of focus values are the following: DOF80 ⫽ ⫺ 1.585C共6, 0兲 ⫹ 0.24C共4, 0兲 ⫺ 0.735C共6, 2兲 ⫺ 0.183C共4, ⫺ 4兲 ⫹ 0.149C共4, 2兲 ⫹ 0.182C共5, ⫺ 5兲 ⫹ 0.468 DOF50 ⫽ 0.638C共4, 0兲 ⫹ 0.565C共4, 2兲 ⫺ 1.815C共6, 0兲 ⫺ 0.155C共3, ⫺ 1兲 ⫺ 0.184C共3, ⫺ 3兲 ⫺ 0.94C共6, 2兲 ⫹ 0.739 In myopic-PRK corneas, 4 Zernike terms significantly contributed to DOF80, with a multiple correlation coefficient value of 0.521, and 3 Zernike terms significantly contributed to DOF50, with a multiple correlation coefficient value of 0.401. Third-order vertical coma (Z(3,⫺1)) and fourthorder tetrafoil (Z(4,4)) were significant contributors to both DOF80 and DOF50. The regression formulas for predicting the depth of focus values are the following:
● ZERNIKE TERMS CONTRIBUTING TO DEPTH OF FOCUS: Table 2 lists the Zernike terms in descending order
of importance that significantly contributed to the depth of focus values for a 6-mm pupil. In normal corneas, 6 Zernike terms significantly contributed to DOF80, with a multiple correlation coefficient value of 0.530, and 6 Zernike terms significantly contributed to DOF50, with a multiple correlation coefficient value of 0.547. Among these Zernike terms, fourth-order 976
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DOF80 ⫽ 1.167C共5, 1兲 ⫺ 0.216C共3, 1兲 ⫹ 0.103C共3, ⫺ 1兲 ⫺ 0.383C共4, 4兲 ⫹ 0.521 OF
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FIGURE 4. In normal corneas, correlation between total corneal higher-order aberrations (HOAs) and DOF80 (Top left) and DOF50 (Top right) for 6-mm pupil (Pearson correlation coefficient r ⴝ 0.303 and r ⴝ 0.382, respectively, both P < .05), and correlation between total HOAs and DOF80 (Bottom left) and DOF50 (Bottom right) for 4-mm pupil (r ⴝ 0.345 and r ⴝ 0.478, respectively, both P < .05). DOF80 ⴝ depth of focus maintaining polychromatic modulation transfer >80% of peak value; DOF50 ⴝ depth of focus maintaining polychromatic modulation transfer >50% of peak value.
DOF50 ⫽ 0.278C共3, ⫺ 1兲 ⫺ 1.001C共4, 4兲 ⫺ 0.503C共3, 3兲 ⫹ 1.009 In hyperopic-LASIK/PRK corneas, 3 Zernike terms significantly contributed to DOF80, with a multiple correlation coefficient value of 0.469, and 6 Zernike terms significantly contributed to DOF50, with a multiple correlation coefficient value of 0.561. Third-order vertical coma (Z(3,⫺1)) and fourth-order astigmatism (Z(4,2)) were significant contributors to both DOF80 and DOF50. The regression formulas for predicting the depth of focus values are the following: DOF80 ⫽ ⫺ 0.251C共3, 1兲 ⫺ 0.144C共3, ⫺ 1兲 ⫺ 0.294C共4, 2兲 ⫹ 0.517 DOF50 ⫽ ⫺ 1.032C共4, 2兲 ⫹ 1.865C共5, ⫺ 3兲 ⫹ 0.453C共4, 0兲 ⫺ 0.277C共3, ⫺ 1兲 ⫹ 1.271C共5, 3兲 ⫹ 1.823C共6, ⫺ 4兲 ⫹ 1.018 For the 4-mm pupil, the multiple correlation coefficient values were smaller than those for the 6-mm pupil. For DOF80 and DOF50, respectively, the multiple correlation coefficient values were 0.288 and 0.396 in normal corneas, 0.474 and 0.390 in myopic-PRK corneas, and 0.342 and 0.206 in hyperopic-LASIK/PRK corneas. Zernike terms that significantly contributed to these correlations are listed in Table 2. VOL. 153, NO. 5
● DEPTH OF FOCUS VS TOTAL HIGHER-ORDER ABERRATIONS AND THIRD-, FOURTH-, FIFTH-, AND SIXTH-OR-
Table 3 shows the Pearson correlation coefficient values between the depth of focus values and wavefront RMS values. In normal corneas, DOF80 and DOF50 values were correlated with HOA values for both 6- and 4-mm pupils. For the 6-mm pupil, DOF80 was weakly correlated with total HOAs, third-order RMS, and fourth-order RMS, and DOF50 was weakly correlated with total HOAs and third- to sixthorder RMS values (all P ⬍ .05 with Bonferroni correction) (Figure 4). For the 4-mm pupil, DOF80 was weakly correlated with total HOAs, third-order RMS, and fifthorder RMS, and DOF50 was weakly correlated with total HOAs and third- to sixth-order RMS values (all P ⬍ .05 with Bonferroni correction). In myopic-PRK corneas, for 6-mm pupils, DOF80 was weakly correlated with total HOAs (r ⫽ 0.300, P ⬍ .05) (Figure 5). For 4-mm pupils, DOF50 was weakly correlated with total HOAs and third-order RMS values (r ⫽ 0.324 and r ⫽ 0.382, both P ⬍ .05 with Bonferroni correction). In hyperopic-LASIK/PRK corneas, for 6-mm pupils, DOF80 was moderately correlated with total HOAs and third-order RMS values (r ⫽ 0.461 and r ⫽ 0.468, respectively, both P ⬍ .05) and DOF50 was moderately correlated with total HOAs and third-order and fourthDER ROOT MEAN SQUARE VALUES:
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FIGURE 5. In myopic-PRK corneas, correlation between total corneal higher-order aberrations (HOAs) and DOF80 (Top left) and DOF50 (Top right) for 6-mm pupil (r ⴝ 0.300, P < .05, and r ⴝ 0.211, P > .05, respectively), and correlation between total HOAs and DOF80 (Bottom left) and DOF50 (Bottom right) for 4-mm pupil (r ⴝ 0.255, P > .05, and r ⴝ 0.324, P < .05, respectively). DOF80 ⴝ depth of focus maintaining polychromatic modulation transfer >80% of peak value; DOF50 ⴝ depth of focus maintaining polychromatic modulation transfer >50% of peak value; PRK ⴝ photorefractive keratectomy.
order RMS values (r ⫽ 0.583, r ⫽ 0.570, and r ⫽ 0.333, respectively, all P ⬍ .05) (Figure 6).
D in myopic-PRK corneas, and 0.6 to 3.5 D in hyperopicLASIK/PRK corneas. Figure 7 shows the corneal wavefront higher-order aberration maps (6-mm) in corneas with the smallest and the largest DOF50 values in each group. The higher-order RMS values ranged from 0.39 to 0.48 m in corneas with the smallest DOF50 values and 0.72 to 0.99 m in corneas with the largest DOF50 values. For the 6-mm pupil, the depth of focus values for myopic-PRK and hyperopic-LASIK/PRK were greater than those for normal corneas, and for the 4-mm pupil, depth of focus values were greater for hyperopic-LASIK/ PRK corneas than those for normal and myopic-PRK corneas, although the differences were small. Based on subjective accommodation, Artola and associates7 reported mean accommodation of 3.2 ⫾ 1.14 D and 3.24 ⫾ 0.99 D in right and left eyes of 10 patients with prior PRK for myopia, and 2.1 ⫾ 0.94 D and 2.3 ⫾ 1.02 D in right and left eyes of 10 control subjects. One explanation for the smaller differences in depth of focus found in our study is that the myopic-PRK patients in our study underwent wavefront-guided procedures, which may have induced smaller increases in HOAs as compared to standard ablations. Also, Artola and associates7 evaluated the total mean subjective accommodation of their patients, which likely results from various factors affecting pseudoaccommodation, while our study only evaluated the con-
DISCUSSION STUDIES HAVE SHOWN THAT APPARENT ACCOMMODATION
is associated with the pupillary diameter and corneal multifocality.2– 4 In this study, we investigated the theoretical pseudoaccommodation of the cornea based on the depth of focus values as calculated from the optical image quality of the anterior corneal surface. We evaluated the corneal optical image quality based on the polychromatic modulation transfer function with Stiles-Crawford effect. The goal was to simulate the image quality that a cornea might experience in the white-light environment. To evaluate the objective depth of focus, we used 2 criteria based on the polychromatic modulation transfer function at 15 cycles/degree, which is equivalent to a visual acuity of 20/40. The overall mean DOF80 and DOF50 values showed small differences among the normal, myopic-PRK, and hyperopic-LASIK/PRK corneas (between 0.02 D and 0.24 D), but there was a large range in the values in each group, especially in corneas with prior hyperopic corneal refractive surgery. As demonstrated by Table 1, the actual ranges of DOF50 were 0.6 to 2.6 D in normal corneas, 0.6 to 2.9 978
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FIGURE 6. In hyperopic-LASIK/PRK corneas, correlation between total corneal higher-order aberrations (HOAs) and DOF80 (Top left) and DOF50 (Top right) for 6-mm pupil (r ⴝ 0.461 and r ⴝ 0.583, respectively, both P < .05), and correlation between total HOAs and DOF80 (Bottom left) and DOF50 (Bottom right) for 4-mm pupil (r ⴝ 0.026 and r ⴝ ⴚ0.020, respectively, both P > .05). DOF80 ⴝ depth of focus maintaining polychromatic modulation transfer >80% of peak value; DOF50 ⴝ depth of focus maintaining polychromatic modulation transfer >50% of peak value; PRK ⴝ photorefractive keratectomy; LASIK ⴝ laser-assisted in situ keratomileusis.
tribution that is potentially provided by the anterior cornea alone. Regarding the correlation between specific Zernike terms and the corneal depth of focus, multiple stepwise regression analyses revealed that certain Zernike terms indeed contributed to the depth of focus with multiple correlation coefficient values of 0.401 to 0.561 for 6-mm pupils but lower values for 4-mm pupils. We have provided the regression formulas to predict the corneal depth of focus values based on the full spectrum of corneal wavefront aberrations. These Zernike terms were different in normal corneas and corneas following myopic or hyperopic corneal refractive surgeries. This is presumably attributable to the altered wavefront aberration profiles induced by the different surgical procedures. In normal corneas, spherical aberration and astigmatism were significant contributors to both DOF80 and DOF50. In myopic-PRK corneas, thirdorder vertical coma and fourth-order tetrafoil were significant contributors to both DOF80 and DOF50. In hyperopic-LASIK/PRK corneas, third-order vertical coma and fourth-order astigmatism were significant contributors to both DOF80 and DOF50. In evaluating the relationship between depth of focus and HOAs, our results demonstrated that depth of focus increased slightly with increasing total HOAs in normal and myopic-PRK corneas, and increased moderately with VOL. 153, NO. 5
increasing total HOAs in hyperopic-LASIK/PRK corneas. The orders that increased the depth of focus were thirdthrough sixth-order RMS for normal corneas, third-order RMS for myopic-PRK corneas, and third- and fourth-order RMS for hyperopic-LASIK/PRK corneas. Our results in normal corneas differ from those reported by Oshika and associates.5 In their study, only coma-like aberrations (third-order RMS) of pseudophakic corneas significantly correlated to the apparent accommodation, as measured by the subjective push-up method. Spherical-like aberrations (fourth-order RMS) did not contribute. Several factors may explain the differences: 1) objective accommodation values assessing the corneal pseudoaccommodation were used in our study; in contrast, subjective accommodation of the eye was used in their study; 2) we calculated corneal wavefront aberrations for 6- and 4-mm zones around the pupil, whereas they analyzed corneal wavefront aberrations within the pupillary area with reported pupillary diameters of 3.51 and 3.53 mm; and 3) normal unoperated corneas were included in our study, while pseudophakic eyes were included in their study; the cataract incision may change the profile of the corneal wavefront aberrations. Marcos and associates14 compared the depth of field of eyes implanted with spherical and aspheric intraocular lenses and found that, although best-corrected optical quality is significantly better with aspheric IOLs possessing
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FIGURE 7. Corneal wavefront higher-order aberration maps (6-mm) in corneas with the smallest DOF50 values (left column) and with the largest DOF values (right column) in normal cornea group (Top), myopic-PRK cornea group (Middle), and hyperopic LASIK/PRK cornea group (Bottom). DOF50 ⴝ depth of focus maintaining polychromatic modulation transfer >50% of peak value; PRK ⴝ photorefractive keratectomy; LASIK ⴝ laser-assisted in situ keratomileusis.
lower fourth-order spherical aberration, the addition of defocus to the eyes caused greater degradation to the optical image quality than that in eyes with spherical IOLs. In a randomized prospective study comparing distancecorrected near and intermediate visual acuity of aspheric and spherical IOLs, Rocha and associates15 reported that eyes implanted with aspheric IOLs had significantly lower overall spherical aberration and worse distance-corrected near visual acuity as compared to eyes with spherical IOLs. These are consistent with our finding that depth of focus increases with the presence of greater fourth-order spherical aberration in normal corneas. The positive correlation between depth of focus and HOAs may be explained by the relative changes of the polychromatic modulation transfer function values observed at best focus and with defocus. In a previous study, we demonstrated that, in a perfect optical system or a system with a low amount of wavefront aberrations, the peak 980
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polychromatic modulation transfer function value is high, and the polychromatic modulation transfer function values drop quickly when defocus is introduced; in contrast, in an optical system with a moderate or large amount of wavefront aberrations, the polychromatic modulation transfer function peak value is relatively low, and these values drop more slowly when defocus is added (unpublished data). Limitations of this study included: 1) this was a theoretical study evaluating the pseudoaccommodation of cornea based on optical image quality of the cornea alone; a clinical study is needed to compare the predicted corneal pseudoaccommodation potential vs the clinical pseudoaccommodative ability of pseudophakic eyes that have monofocal IOLs; 2) the myopic group consisted only of wavefront-guided PRK corneas, whereas wavefront-guided PRK/LASIK and standard LASIK corneas were included in the hyperopic group, because of the small number of wavefront-guided PRK corneas that met the inclusion OF
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criteria (18 corneas); and 3) data were derived from Placido images of the anterior corneal surface and are therefore limited by this imaging methodology and the absence of data from the posterior corneal surface.
In conclusion, corneal wavefront aberrations play a role in corneal pseudoaccommodation. The modification of corneal aberrations by excimer laser corneal surgery tends to increase corneal pseudoaccommodation.
PUBLICATION OF THIS ARTICLE WAS SUPPORTED IN PART BY AN UNRESTRICTED GRANT FROM RESEARCH TO PREVENT Blindness, New York, New York. The authors do not indicate any financial conflict of interest related to this study. Involved in design of the study (E.Y., L.W., D.D.K.); conduct of the study (E.Y., L.W., D.D.K.); collection, management, analysis, and interpretation of data (E.Y., L.W., D.D.K.); and preparation, review, or approval of the manuscript (E.Y., L.W., D.D.K.). This retrospective study was approved by the Institutional Review Board of Baylor College of Medicine, Houston, Texas.
REFERENCES 1. Huber C. Planned myopic astigmatism as a substitute for accommodation in pseudophakia. J Am Intraocul Implant Soc 1981;7(3):244 –249. 2. Nakazawa M, Ohtsuki K. Apparent accommodation in pseudophakic eyes after implantation of posterior chamber intraocular lenses. Am J Ophthalmol 1983;96(4):435– 438. 3. Nakazawa M, Ohtsuki K. Apparent accommodation in pseudophakic eyes after implantation of posterior chamber intraocular lenses: optical analysis. Invest Ophthalmol Vis Sci 1984;25(12):1458 –1460. 4. Fukuyama M, Oshika T, Amano S, Yoshitomi F. Relationship between apparent accomodation and corneal multifocality in pseudophakic eyes. Ophthalmology 1999;106(6): 1178 –1181. 5. Oshika T, Mimura T, Tanaka S, et al. Apparent accommodation and corneal wavefront aberration in pseudophakic eyes. Invest Ophthalmol Vis Sci 2002;43(9):2882–2886. 6. Nio YK, Jansonius NM, Wijdh RH, et al. Effect of methods of myopia correction on visual acuity, contrast sensitivity, and depth of focus. J Cataract Refract Surg 2003;29(11): 2082–2095. 7. Artola A, Patel S, Schimchak P, Ayala MJ, Ruiz-Moreno JM, Alió JL. Evidence for delayed presbyopia after photorefractive keratectomy for myopia. Ophthalmology 2006;113(5): 735–741.e1.
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8. Thibos LN, Applegate RA, Schwiegerling JT, et al. Standards for reporting the optical aberrations of eyes. In: MacRae SM, Krueger RR, Applegate RA, eds. Customized Corneal Ablation, the Quest for Supervision. Thorofare: Slack Inc, 2001:348 –361. 9. Dai GM. Optical surface optimization for the correction of presbyopia. Appl Opt 2006;45:4184 – 4195. 10. Applegate RA, Ballentine C, Gross H, Sarver EJ, Sarver CA. Visual acuity as a function of Zernike mode and level of root mean square error. Optom Vis Sci 2003;80(2):97–105. 11. Marcos S, Moreno E, Navarro R. The depth-of-field of the human eye from objective and subjective measurements. Vision Res 1999;39(12):2039 –2049. 12. Legge GE, Mullen KT, Woo GC, Campbell FW. Tolerance to visual defocus. J Opt Soc Am A 1987;4(5):851– 863. 13. Smolek MK, Klyce SD, Sarver EJ. Inattention to nonsuperimposable midline symmetry causes wavefront analysis error. Arch Ophthalmol 2002;120(4):439 – 447. 14. Marcos S, Barbero S, Jiménez-Alfaro I. Optical quality and depth-of-field of eyes implanted with spherical and aspheric intraocular lenses. J Refract Surg 2005;21(3):223– 235. 15. Rocha KM, Soriano ES, Chamon W, Chalita MR, Nosé W. Spherical aberration and depth of focus in eyes implanted with aspheric and spherical intraocular lenses: a prospective randomized study. Ophthalmology 2007;114(11):2050 – 2054.
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Biosketch Elizabeth Yeu received her Doctorate of Medicine through an accelerated undergraduate studies and medical school program from the University of Florida College of Medicine in 2003. She completed an ophthalmology residency at the Rush University Medical Center in Chicago, Illinois, where she served as the chief resident. Following residency training, Dr Yeu completed her fellowship in cornea, anterior segment and refractive surgery at the Cullen Eye Institute, Baylor College of Medicine, where she is currently an Assistant Professor in the Department of Ophthalmology. Her areas of interest reflect both the cornea and refractive surgery specialties, including advanced options in the treatment of keratoconus and innovations in cataract and refractive procedures. Dr Yeu currently serves on the Young Physicians Committee of the American Society of Cataract, the Ophthalmic News and Education Refractive subcommittee and the Refractive Surgery Annual Meeting subcommittee of the American Academy of Ophthalmology. She has authored several journal publications and book chapters, including monographs on astigmatism management, and novel lens implant options for cataract surgery.
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Biosketch Li Wang, MD, PhD, is a Assistant Professor at the Cullen Eye Institute, Department of Ophthalmology, Baylor College of Medicine. Her research interests are focused on cataract and refractive surgery.
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To determine the effect on corneal pseudoaccommodation of anterior corneal wavefront aberrations in normal corneas and corneas with prior myopic or hyperopic photorefractive keratectomy (PRK) or laserassisted in situ keratomileusis (LASIK). ● DESIGN: Theoretical study. ● METHODS: In 220 normal eyes, 102 myopic-PRK eyes, and 106 hyperopic-LASIK/PRK eyes, anterior corneal higher-order aberrations (HOAs, third to sixth order, 6and 4-mm pupils) were computed from the Atlas corneal elevation data using the VOL-CT program. Using the ZernikeTool, corneal optical image quality was evaluated by the polychromatic modulation transfer function with Stiles-Crawford effect. Defocus from ⴚ3.0 diopters (D) to ⴙ3.0 D was added to corneal HOAs, and depth of focus was defined as the ranges over which the polychromatic modulation transfer function maintains 80% of the peak value (DOF80) and 50% of the peak value (DOF50). The depth of focus values between groups were compared, stepwise multiple regression was used to assess if any Zernike terms significantly contributed to the depth of focus, and correlation analysis was performed to evaluate the correlation between depth of focus and corneal HOAs. ● RESULTS: The depth of focus varied widely between corneas, especially in corneas with prior hyperopicLASIK/PRK. For 6-mm pupil, mean depth of focus values in myopic-PRK and hyperopic-LASIK/PRK corneas were significantly greater than those for normal corneas, and for 4-mm pupil, depth of focus values in hyperopic-LASIK/PRK corneas were greater than those in normal and myopic-PRK corneas. Zernike terms significantly contributing to both DOF80 and DOF50 were fourth- and sixth-order spherical aberration and fourth- and sixth-order astigmatism in normal corneas, third-order vertical coma and fourth-order tetrafoil in myopic-PRK corneas, and third-order vertical coma and fourth-order astigmatism in hyperopic-LASIK/ PRK corneas. Depth of focus had weak to moderate positive correlation with HOAs (Pearson correlation coefficient r ranged from 0.300 to 0.583). Accepted for publication Oct 17, 2011. From the Cullen Eye Institute, Department of Ophthalmology, Baylor College of Medicine, Houston, Texas. Inquiries to Elizabeth Yeu, Department of Ophthalmology, Baylor College of Medicine, 6565 Fannin, NC205, Houston, TX 77030; e-mail: [email protected]
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● CONCLUSION:
These theoretical calculations suggest that certain corneal wavefront aberrations affect corneal pseudoaccommodation. To predict corneal pseudoaccommodation, the most important Zernike term is spherical aberration in normal eyes and coma in eyes with prior laser corneal surgery. (Am J Ophthalmol 2012;153: 972–981. © 2012 by Elsevier Inc. All rights reserved.)
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tion of a monofocal intraocular lens (IOL), some patients attain surprisingly good uncorrected near and distance vision. This phenomenon is referred to as apparent accommodation1 or pseudoaccommodation. Studies have shown that the pseudoaccommodation is inversely proportional to the pupillary diameter and positively correlated with the depth of field and corneal multifocality.2– 4 Oshika and associates assessed in pseudophakic eyes the relationship between apparent accommodation and wavefront aberrations of the cornea.5 They found that the root mean square values of the total third-order (coma-like) aberrations of the cornea were significantly correlated to the apparent accommodation. Evidence for the cornea’s role in pseudoaccommodation has also been noted in eyes that have undergone myopic corneal refractive surgery, with treated patients demonstrating enhanced distancecorrected near acuity and greater measured accommodative range.6,7 Pseudoaccommodation has been traditionally studied using subjective measurements. The purpose of this theoretical study was to assess potential corneal pseudoaccommodation as expressed by calculated depth of focus values and to correlate specific higher-order aberrations (HOAs) to the corneal depth of focus values that were calculated from the corneas of eyes in the cataract population, as well as in eyes following myopic and hyperopic excimer laser ablation.
PATIENTS AND METHODS ● PATIENTS: We included data from 3 groups of patients who visited our clinic or underwent myopic or hyperopic photorefractive keratectomy (PRK) or laser-assisted in situ keratomileusis (LASIK) between May 2002 and March 2007. The first group included 220 eyes of 137 patients, aged 40 to 80 years, with no prior corneal surgery. These subjects were selected from our preoperative cataract
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FIGURE 1. Corneal wavefront aberrations in normal, myopicPRK, and hyperopic-LASIK/PRK corneas for 6-mm pupil (Top) and 4-mm pupil (Bottom) (*: significant difference between myopic-PRK corneas and normal cornea; ⽥: significant difference between hyperopic-LASIK/PRK corneas and normal cornea, all P < .05 with Bonferroni correction). PRK ⴝ photorefractive keratectomy; LASIK ⴝlaser-assisted in situ keratomileusis.
patients, and their corneas were measured before undergoing cataract surgery. The second group had 102 eyes of 77 patients, aged 22 to 45 years, who underwent wavefrontguided myopic-PRK by 1 surgeon using the CustomVue STAR laser system (Abbott Medical Optics Inc [AMO], Santa Ana, California, USA) and who had 6 months of follow-up. Lastly, the third group included 106 eyes of 80 patients aged 40 to 59 years who underwent standard (81 eyes) or wavefront-guided (7 eyes) hyperopic-LASIK or wavefront-guided hyperopic-PRK (18 eyes) by 1 surgeon using the AMO STAR laser system. Minimum follow-up was 3 months for LASIK eyes and 6 months for PRK eyes. Inclusion criteria included: 1) no corneal pathology; 2) no prior contact lens wear or wear discontinued 4 weeks for rigid gas permeable lens, 3 weeks for toric soft contact lenses, and 2 weeks for soft contact lenses; and 3) Humphrey Atlas corneal topographic maps with no missing data points within the central 7-mm zone (Carl Zeiss Inc, Pleasanton, California, USA). VOL. 153, NO. 5
FIGURE 2. Box plot of corneal pseudoaccommodation depth of focus (DOF) values for 6-mm pupil (Top) and 4-mm pupil (Bottom). DOF80 ⴝ depth of focus maintaining polychromatic modulation transfer >80% of peak value; DOF50 ⴝ depth of focus maintaining polychromatic modulation transfer >50% of peak value; PRK ⴝ photorefractive keratectomy; LASIK ⴝ laser-assisted in situ keratomileusis.
In the myopic and hyperopic groups, we included corneas with different procedures. In our clinic, during that period of time, wavefront-guided myopic-PRK was the dominant procedure for myopic corneal laser surgery. Because of the later approval of the wavefront-guided LASIK for hyperopia by the Food and Drug Administration, the majority of the eyes in the hyperopic group had undergone conventional hyperopic LASIK. ● DEPTH OF FOCUS ON THE CORNEA:
Corneal wavefront aberrations up to sixth order for 6- and 4-mm pupils were computed from Humphrey Atlas corneal elevation data using the VOL-CT program (Sarver and Associates Inc, Carbondale, Illinois, USA), which uses the standards for calculation and reporting the optical aberrations of eyes as proposed by Thibos and associates.8 The topographic maps were recentered around the entrance pupil, and wavefront aberrations
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FIGURE 3. Percentage of eyes with certain amount of corneal pseudoaccommodation depth of focus evaluated by DOF80 (Top left) and DOF50 (Top right) for 6-mm pupil and DOF80 (Bottom left) and DOF50 (Bottom right) for 4-mm pupil. DOF80 ⴝ depth of focus maintaining polychromatic modulation transfer >80% of peak value; DOF50 ⴝ depth of focus maintaining polychromatic modulation transfer >50% of peak value; PRK ⴝ photorefractive keratectomy; LASIK ⴝ laser-assisted in situ keratomileusis.
from the cornea were calculated using a corneal refractive index of 1.376 for the wavelength of 555 nm. Corneal optical image quality was evaluated by the polychromatic modulation transfer function with StilesCrawford effect. The polychromatic modulation transfer function was calculated using the ZernikeTool program (Abbott Medical Optics Inc).9 With this program, 7 wavelengths (400, 450, 500, 550, 600, 650, and 700 nm) were used to represent the visible spectrum, and the polychromatic point spread function with Stiles-Crawford effect was weighted in the imaging plane based on the retinal spectral response function. To evaluate the effect of defocus on corneal image quality, defocus from ⫺3.0 diopters (D) to ⫹3.0 D in 0.1-D intervals was added to the HOAs of the corneas. Desired defocus in diopter was converted to wavefront coefficient in m and added to the second-order defocus term using the following equation derived from the method described by Applegate and associates:10 974
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C02 ⫽
SR2 ⫺ 4兹3
where C20 is the Zernike coefficient in m for the second-order defocus term, S is the dioptric power of the sphere expressed in diopter, and R is the radius of the pupil expressed in mm. The polychromatic modulation transfer function at 15 cycles/degree (equivalent to visual acuity of 20/40 object) was used, and depth of focus was defined by 2 criteria based on the polychromatic modulation transfer function at 15 cycles/degree: 1) the range over which the polychromatic modulation transfer function maintains 80% of the peak value (DOF80);11 and 2) the range over which the polychromatic modulation transfer function maintains 50% of the peak value (DOF50)12 (this criterion represents a 50% drop in image quality, which could still provide adequate near acuity). OF
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TABLE 1. Corneal Pseudoaccommodation Depth of Focus Values in Each Group (Mean ⫾ SD, [range]) 6-mm Pupil Group
Normal corneas (n ⫽ 220) Myopic-PRK corneas (n ⫽ 102) Hyperopic-LASIK/PRK corneas (n ⫽ 106)
4-mm Pupil
DOF80 (D)
DOF50 (D)
DOF80 (D)
DOF50 (D)
0.53 ⫾ 0.08 (0.4 to 0.8) 0.57 ⫾ 0.13a (0.4 to 1.3) 0.61 ⫾ 0.20a (0.3 to 1.4)
0.96 ⫾ 0.15 (0.6 to 1.7) 1.04 ⫾ 0.25b (0.6 to 2.4) 1.18 ⫾ 0.43b (0.6 to 2.7)
0.55 ⫾ 0.14c (0.4 to 1.4) 0.55 ⫾ 0.15c (0.3 to 1.4) 0.63 ⫾ 0.22 (0.4 to 1.5)
1.03 ⫾ 0.34d (0.7 to 2.6) 1.05 ⫾ 0.40d (0.6 to 2.9) 1.27 ⫾ 0.51 (0.7 to 3.5)
D ⫽ diopters; DOF50 ⫽ depth of focus maintaining polychromatic modulation transfer ⱖ50% of peak value; DOF80 ⫽ depth of focus maintaining polychromatic modulation transfer ⱖ80% of peak value; LASIK ⫽ laser-assisted in situ keratomileusis; PRK ⫽ photorefractive keratectomy. a,b,c,d For each criterion, depths of focus between groups were significantly different except for pair with a,b,c,d (all P ⬍ .05 with Bonferroni correction).
TABLE 2. Corneal Wavefront Zernike Terms Significantly Contributing to the Corneal Pseudoaccommodation Depth of Focus Values for 6-mm Pupil Group
Normal corneas Myopic-PRK corneas Hyperopic-LASIK/PRK corneas
Criterion
Multiple Correlation Coefficient R
Zernike Terms in Descending Order of Importance
DOF80 DOF50 DOF80 DOF50 DOF80 DOF50
0.530 0.547 0.521 0.401 0.469 0.561
Z(6,0), Z(4,0), Z(6,2), Z(4,⫺4), Z(4,2), and Z(5,⫺5) Z(4,0), Z(4,2), Z(6,0), Z(3,⫺1), Z(3,⫺3), and Z(6,2) Z(5,1), Z(3,1), Z(3,⫺1), and Z(4,4) Z(3,⫺1), Z(4,4), and Z(3,3) Z(3,1), Z(3,⫺1), and Z(4,2) Z(4,2), Z(5,⫺3), Z(4,0), Z(3,⫺1), Z(5,3), and Z(6,⫺4)
DOF50 ⫽ depth of focus maintaining polychromatic modulation transfer ⱖ50% of peak value; DOF80 ⫽ depth of focus maintaining polychromatic modulation transfer ⱖ80% of peak value; LASIK ⫽ laser-assisted in situ keratomileusis; PRK ⫽ photorefractive keratectomy.
● STATISTICAL ANALYSIS: The depth of focus values between groups were compared using Mann-Whitney test. Correlation analysis was performed to evaluate the correlation between depth of focus and root mean square (RMS) values of total higher-order aberrations (HOAs, third to sixth order) and third-order, fourth-order, fifthorder, and sixth-order wavefront aberrations of the cornea. Stepwise multiple regression was used to assess if any Zernike terms significantly contributed to the depth of focus. For this purpose, for the left eyes, Zernike coefficients for these Zernike terms with mirror symmetry between both eyes were flipped to match the right eye.13 SPSS 15.0 for Windows (SPSS Inc, Chicago, Illinois, USA) was used for statistical analysis. The Bonferroni correction was employed for multiple tests. A probability of less than 5% (P ⬍ .05) was considered statistically significant.
RESULTS ● CORNEAL ZERNIKE COEFFICIENTS:
Figure 1 shows the corneal HOAs in normal, myopic-PRK, and hyperopicLASIK/PRK corneas. Compared to normal corneas, for a 6-mm pupil, myopic-PRK and hyperopic-LASIK/PRK cor-
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neas each had significantly different mean coefficient values for 6 Zernike terms: Z(3,⫺3), Z(3,3), Z(4,⫺4), Z(4,0), Z(5,1), and Z(6,0) for myopia and Z(3,⫺3), Z(3,1), Z(3,3), Z(4,0), Z(4,4), and Z(5,1) for hyperopia (Figure 1, Top). For a 4-mm pupil, compared to normal corneas, ablated corneas had significantly different mean coefficient values for 2 Zernike terms: Z(3,⫺3) and Z(6,0) for myopicPRK corneas and Z(3,⫺3) and Z(4,0) for hyperopicLASIK/PRK corneas (Figure 1, Bottom) (all P ⬍ .05 with Bonferroni correction). ● DEPTH OF FOCUS VALUES:
The depth of focus varied widely among corneas, especially in corneas with prior hyperopic-LASIK/PRK (Figure 2). The distributions of the depth of focus values are shown in Figure 3. Table 1 shows the depth of focus values in each group. There were no significant differences in mean depth of focus values between the 6-mm pupil and 4-mm pupil within each group of eyes. The mean DOF80 and DOF50 values for myopic-PRK corneas were greater than those for normal corneas by 0.04 D and 0.08 D for the 6-mm pupil (both P ⬍ .05 with Bonferroni correction) and by 0.00 D and 0.02 D for the 4-mm pupil, respectively (both P ⬎ .05 with Bonferroni correction). The mean DOF80 and
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TABLE 3. Pearson Correlation Coefficient Values Between Corneal Pseudoaccommodation Depth of Focus Values and Corneal Wavefront Root Mean Square Values RMS Values
Normal corneas 6-mm pupil DOF80 DOF50 4-mm pupil DOF80 DOF50 Myopic-PRK corneas 6-mm pupil DOF80 DOF50 4-mm pupil DOF80 DOF50 Hyperopic-LASIK/PRK corneas 6-mm pupil DOF80 DOF50 4-mm pupil DOF80 DOF50
HOAs RMS
Third-order RMS
Fourth-order RMS
Fifth-order RMS
Sixth-order RMS
0.303a 0.382a
0.227a 0.257a
0.221a 0.326a
0.164 0.261a
0.200 0.224a
0.345a 0.478a
0.323a 0.379a
0.198 0.311a
0.230a 0.439a
0.188 0.326a
0.300a 0.211
0.240 0.203
0.221 0.101
0.248 0.259
0.121 0.137
0.255 0.324a
0.230 0.382a
0.239 0.126
0.128 0.065
0.003 0.043
0.461a 0.583a
0.468a 0.570a
0.228 0.333a
0.073 0.171
0.146 0.230
0.040 ⫺0.016
0.172 0.080
0.026 ⫺0.020
⫺0.020 ⫺0.069
0.014 0.004
DOF50 ⫽ depth of focus maintaining polychromatic modulation transfer ⱖ50% of peak value; DOF80 ⫽ depth of focus maintaining polychromatic modulation transfer ⱖ80% of peak value; HOAs ⫽ higher-order aberrations; LASIK ⫽ laser-assisted in situ keratomileusis; PRK ⫽ photorefractive keratectomy; RMS ⫽ root mean square. a Significant correlation (P ⬍ .05 with Bonferroni correction).
DOF50 values for hyperopic LASIK/PRK corneas were greater than those for normal corneas by 0.08 D and 0.22 D for the 6-mm pupil (both P ⬍ .05 with Bonferroni correction) and by 0.08 D and 0.24 D for the 4-mm pupil respectively (both P ⬍ .05 with Bonferroni correction). Lastly, the mean DOF80 and DOF50 values for hyperopic LASIK/PRK corneas were greater than those for myopicPRK corneas by 0.04 D and 0.14 D for the 6-mm pupil (both P ⬎ .05 with Bonferroni correction) and by 0.08 D and 0.22 D for the 4-mm pupil (both P ⬍ .05 with Bonferroni correction). Although not demonstrated in Table 1, in the hyperopic-LASIK/PRK group, there were no differences between depth of focus values among corneas that underwent prior standard LASIK, wavefrontguided LASIK, or wavefront-guided PRK (all P ⬎ .05 with Bonferroni correction).
spherical aberration (Z(4,0)) and astigmatism (Z(4,2)) and sixth-order spherical aberration (Z(6,0)) and astigmatism (Z(6,2)) were significant contributors to both DOF80 and DOF50. The regression formulas for predicting the depth of focus values are the following: DOF80 ⫽ ⫺ 1.585C共6, 0兲 ⫹ 0.24C共4, 0兲 ⫺ 0.735C共6, 2兲 ⫺ 0.183C共4, ⫺ 4兲 ⫹ 0.149C共4, 2兲 ⫹ 0.182C共5, ⫺ 5兲 ⫹ 0.468 DOF50 ⫽ 0.638C共4, 0兲 ⫹ 0.565C共4, 2兲 ⫺ 1.815C共6, 0兲 ⫺ 0.155C共3, ⫺ 1兲 ⫺ 0.184C共3, ⫺ 3兲 ⫺ 0.94C共6, 2兲 ⫹ 0.739 In myopic-PRK corneas, 4 Zernike terms significantly contributed to DOF80, with a multiple correlation coefficient value of 0.521, and 3 Zernike terms significantly contributed to DOF50, with a multiple correlation coefficient value of 0.401. Third-order vertical coma (Z(3,⫺1)) and fourthorder tetrafoil (Z(4,4)) were significant contributors to both DOF80 and DOF50. The regression formulas for predicting the depth of focus values are the following:
● ZERNIKE TERMS CONTRIBUTING TO DEPTH OF FOCUS: Table 2 lists the Zernike terms in descending order
of importance that significantly contributed to the depth of focus values for a 6-mm pupil. In normal corneas, 6 Zernike terms significantly contributed to DOF80, with a multiple correlation coefficient value of 0.530, and 6 Zernike terms significantly contributed to DOF50, with a multiple correlation coefficient value of 0.547. Among these Zernike terms, fourth-order 976
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DOF80 ⫽ 1.167C共5, 1兲 ⫺ 0.216C共3, 1兲 ⫹ 0.103C共3, ⫺ 1兲 ⫺ 0.383C共4, 4兲 ⫹ 0.521 OF
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FIGURE 4. In normal corneas, correlation between total corneal higher-order aberrations (HOAs) and DOF80 (Top left) and DOF50 (Top right) for 6-mm pupil (Pearson correlation coefficient r ⴝ 0.303 and r ⴝ 0.382, respectively, both P < .05), and correlation between total HOAs and DOF80 (Bottom left) and DOF50 (Bottom right) for 4-mm pupil (r ⴝ 0.345 and r ⴝ 0.478, respectively, both P < .05). DOF80 ⴝ depth of focus maintaining polychromatic modulation transfer >80% of peak value; DOF50 ⴝ depth of focus maintaining polychromatic modulation transfer >50% of peak value.
DOF50 ⫽ 0.278C共3, ⫺ 1兲 ⫺ 1.001C共4, 4兲 ⫺ 0.503C共3, 3兲 ⫹ 1.009 In hyperopic-LASIK/PRK corneas, 3 Zernike terms significantly contributed to DOF80, with a multiple correlation coefficient value of 0.469, and 6 Zernike terms significantly contributed to DOF50, with a multiple correlation coefficient value of 0.561. Third-order vertical coma (Z(3,⫺1)) and fourth-order astigmatism (Z(4,2)) were significant contributors to both DOF80 and DOF50. The regression formulas for predicting the depth of focus values are the following: DOF80 ⫽ ⫺ 0.251C共3, 1兲 ⫺ 0.144C共3, ⫺ 1兲 ⫺ 0.294C共4, 2兲 ⫹ 0.517 DOF50 ⫽ ⫺ 1.032C共4, 2兲 ⫹ 1.865C共5, ⫺ 3兲 ⫹ 0.453C共4, 0兲 ⫺ 0.277C共3, ⫺ 1兲 ⫹ 1.271C共5, 3兲 ⫹ 1.823C共6, ⫺ 4兲 ⫹ 1.018 For the 4-mm pupil, the multiple correlation coefficient values were smaller than those for the 6-mm pupil. For DOF80 and DOF50, respectively, the multiple correlation coefficient values were 0.288 and 0.396 in normal corneas, 0.474 and 0.390 in myopic-PRK corneas, and 0.342 and 0.206 in hyperopic-LASIK/PRK corneas. Zernike terms that significantly contributed to these correlations are listed in Table 2. VOL. 153, NO. 5
● DEPTH OF FOCUS VS TOTAL HIGHER-ORDER ABERRATIONS AND THIRD-, FOURTH-, FIFTH-, AND SIXTH-OR-
Table 3 shows the Pearson correlation coefficient values between the depth of focus values and wavefront RMS values. In normal corneas, DOF80 and DOF50 values were correlated with HOA values for both 6- and 4-mm pupils. For the 6-mm pupil, DOF80 was weakly correlated with total HOAs, third-order RMS, and fourth-order RMS, and DOF50 was weakly correlated with total HOAs and third- to sixthorder RMS values (all P ⬍ .05 with Bonferroni correction) (Figure 4). For the 4-mm pupil, DOF80 was weakly correlated with total HOAs, third-order RMS, and fifthorder RMS, and DOF50 was weakly correlated with total HOAs and third- to sixth-order RMS values (all P ⬍ .05 with Bonferroni correction). In myopic-PRK corneas, for 6-mm pupils, DOF80 was weakly correlated with total HOAs (r ⫽ 0.300, P ⬍ .05) (Figure 5). For 4-mm pupils, DOF50 was weakly correlated with total HOAs and third-order RMS values (r ⫽ 0.324 and r ⫽ 0.382, both P ⬍ .05 with Bonferroni correction). In hyperopic-LASIK/PRK corneas, for 6-mm pupils, DOF80 was moderately correlated with total HOAs and third-order RMS values (r ⫽ 0.461 and r ⫽ 0.468, respectively, both P ⬍ .05) and DOF50 was moderately correlated with total HOAs and third-order and fourthDER ROOT MEAN SQUARE VALUES:
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FIGURE 5. In myopic-PRK corneas, correlation between total corneal higher-order aberrations (HOAs) and DOF80 (Top left) and DOF50 (Top right) for 6-mm pupil (r ⴝ 0.300, P < .05, and r ⴝ 0.211, P > .05, respectively), and correlation between total HOAs and DOF80 (Bottom left) and DOF50 (Bottom right) for 4-mm pupil (r ⴝ 0.255, P > .05, and r ⴝ 0.324, P < .05, respectively). DOF80 ⴝ depth of focus maintaining polychromatic modulation transfer >80% of peak value; DOF50 ⴝ depth of focus maintaining polychromatic modulation transfer >50% of peak value; PRK ⴝ photorefractive keratectomy.
order RMS values (r ⫽ 0.583, r ⫽ 0.570, and r ⫽ 0.333, respectively, all P ⬍ .05) (Figure 6).
D in myopic-PRK corneas, and 0.6 to 3.5 D in hyperopicLASIK/PRK corneas. Figure 7 shows the corneal wavefront higher-order aberration maps (6-mm) in corneas with the smallest and the largest DOF50 values in each group. The higher-order RMS values ranged from 0.39 to 0.48 m in corneas with the smallest DOF50 values and 0.72 to 0.99 m in corneas with the largest DOF50 values. For the 6-mm pupil, the depth of focus values for myopic-PRK and hyperopic-LASIK/PRK were greater than those for normal corneas, and for the 4-mm pupil, depth of focus values were greater for hyperopic-LASIK/ PRK corneas than those for normal and myopic-PRK corneas, although the differences were small. Based on subjective accommodation, Artola and associates7 reported mean accommodation of 3.2 ⫾ 1.14 D and 3.24 ⫾ 0.99 D in right and left eyes of 10 patients with prior PRK for myopia, and 2.1 ⫾ 0.94 D and 2.3 ⫾ 1.02 D in right and left eyes of 10 control subjects. One explanation for the smaller differences in depth of focus found in our study is that the myopic-PRK patients in our study underwent wavefront-guided procedures, which may have induced smaller increases in HOAs as compared to standard ablations. Also, Artola and associates7 evaluated the total mean subjective accommodation of their patients, which likely results from various factors affecting pseudoaccommodation, while our study only evaluated the con-
DISCUSSION STUDIES HAVE SHOWN THAT APPARENT ACCOMMODATION
is associated with the pupillary diameter and corneal multifocality.2– 4 In this study, we investigated the theoretical pseudoaccommodation of the cornea based on the depth of focus values as calculated from the optical image quality of the anterior corneal surface. We evaluated the corneal optical image quality based on the polychromatic modulation transfer function with Stiles-Crawford effect. The goal was to simulate the image quality that a cornea might experience in the white-light environment. To evaluate the objective depth of focus, we used 2 criteria based on the polychromatic modulation transfer function at 15 cycles/degree, which is equivalent to a visual acuity of 20/40. The overall mean DOF80 and DOF50 values showed small differences among the normal, myopic-PRK, and hyperopic-LASIK/PRK corneas (between 0.02 D and 0.24 D), but there was a large range in the values in each group, especially in corneas with prior hyperopic corneal refractive surgery. As demonstrated by Table 1, the actual ranges of DOF50 were 0.6 to 2.6 D in normal corneas, 0.6 to 2.9 978
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FIGURE 6. In hyperopic-LASIK/PRK corneas, correlation between total corneal higher-order aberrations (HOAs) and DOF80 (Top left) and DOF50 (Top right) for 6-mm pupil (r ⴝ 0.461 and r ⴝ 0.583, respectively, both P < .05), and correlation between total HOAs and DOF80 (Bottom left) and DOF50 (Bottom right) for 4-mm pupil (r ⴝ 0.026 and r ⴝ ⴚ0.020, respectively, both P > .05). DOF80 ⴝ depth of focus maintaining polychromatic modulation transfer >80% of peak value; DOF50 ⴝ depth of focus maintaining polychromatic modulation transfer >50% of peak value; PRK ⴝ photorefractive keratectomy; LASIK ⴝ laser-assisted in situ keratomileusis.
tribution that is potentially provided by the anterior cornea alone. Regarding the correlation between specific Zernike terms and the corneal depth of focus, multiple stepwise regression analyses revealed that certain Zernike terms indeed contributed to the depth of focus with multiple correlation coefficient values of 0.401 to 0.561 for 6-mm pupils but lower values for 4-mm pupils. We have provided the regression formulas to predict the corneal depth of focus values based on the full spectrum of corneal wavefront aberrations. These Zernike terms were different in normal corneas and corneas following myopic or hyperopic corneal refractive surgeries. This is presumably attributable to the altered wavefront aberration profiles induced by the different surgical procedures. In normal corneas, spherical aberration and astigmatism were significant contributors to both DOF80 and DOF50. In myopic-PRK corneas, thirdorder vertical coma and fourth-order tetrafoil were significant contributors to both DOF80 and DOF50. In hyperopic-LASIK/PRK corneas, third-order vertical coma and fourth-order astigmatism were significant contributors to both DOF80 and DOF50. In evaluating the relationship between depth of focus and HOAs, our results demonstrated that depth of focus increased slightly with increasing total HOAs in normal and myopic-PRK corneas, and increased moderately with VOL. 153, NO. 5
increasing total HOAs in hyperopic-LASIK/PRK corneas. The orders that increased the depth of focus were thirdthrough sixth-order RMS for normal corneas, third-order RMS for myopic-PRK corneas, and third- and fourth-order RMS for hyperopic-LASIK/PRK corneas. Our results in normal corneas differ from those reported by Oshika and associates.5 In their study, only coma-like aberrations (third-order RMS) of pseudophakic corneas significantly correlated to the apparent accommodation, as measured by the subjective push-up method. Spherical-like aberrations (fourth-order RMS) did not contribute. Several factors may explain the differences: 1) objective accommodation values assessing the corneal pseudoaccommodation were used in our study; in contrast, subjective accommodation of the eye was used in their study; 2) we calculated corneal wavefront aberrations for 6- and 4-mm zones around the pupil, whereas they analyzed corneal wavefront aberrations within the pupillary area with reported pupillary diameters of 3.51 and 3.53 mm; and 3) normal unoperated corneas were included in our study, while pseudophakic eyes were included in their study; the cataract incision may change the profile of the corneal wavefront aberrations. Marcos and associates14 compared the depth of field of eyes implanted with spherical and aspheric intraocular lenses and found that, although best-corrected optical quality is significantly better with aspheric IOLs possessing
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FIGURE 7. Corneal wavefront higher-order aberration maps (6-mm) in corneas with the smallest DOF50 values (left column) and with the largest DOF values (right column) in normal cornea group (Top), myopic-PRK cornea group (Middle), and hyperopic LASIK/PRK cornea group (Bottom). DOF50 ⴝ depth of focus maintaining polychromatic modulation transfer >50% of peak value; PRK ⴝ photorefractive keratectomy; LASIK ⴝ laser-assisted in situ keratomileusis.
lower fourth-order spherical aberration, the addition of defocus to the eyes caused greater degradation to the optical image quality than that in eyes with spherical IOLs. In a randomized prospective study comparing distancecorrected near and intermediate visual acuity of aspheric and spherical IOLs, Rocha and associates15 reported that eyes implanted with aspheric IOLs had significantly lower overall spherical aberration and worse distance-corrected near visual acuity as compared to eyes with spherical IOLs. These are consistent with our finding that depth of focus increases with the presence of greater fourth-order spherical aberration in normal corneas. The positive correlation between depth of focus and HOAs may be explained by the relative changes of the polychromatic modulation transfer function values observed at best focus and with defocus. In a previous study, we demonstrated that, in a perfect optical system or a system with a low amount of wavefront aberrations, the peak 980
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polychromatic modulation transfer function value is high, and the polychromatic modulation transfer function values drop quickly when defocus is introduced; in contrast, in an optical system with a moderate or large amount of wavefront aberrations, the polychromatic modulation transfer function peak value is relatively low, and these values drop more slowly when defocus is added (unpublished data). Limitations of this study included: 1) this was a theoretical study evaluating the pseudoaccommodation of cornea based on optical image quality of the cornea alone; a clinical study is needed to compare the predicted corneal pseudoaccommodation potential vs the clinical pseudoaccommodative ability of pseudophakic eyes that have monofocal IOLs; 2) the myopic group consisted only of wavefront-guided PRK corneas, whereas wavefront-guided PRK/LASIK and standard LASIK corneas were included in the hyperopic group, because of the small number of wavefront-guided PRK corneas that met the inclusion OF
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criteria (18 corneas); and 3) data were derived from Placido images of the anterior corneal surface and are therefore limited by this imaging methodology and the absence of data from the posterior corneal surface.
In conclusion, corneal wavefront aberrations play a role in corneal pseudoaccommodation. The modification of corneal aberrations by excimer laser corneal surgery tends to increase corneal pseudoaccommodation.
PUBLICATION OF THIS ARTICLE WAS SUPPORTED IN PART BY AN UNRESTRICTED GRANT FROM RESEARCH TO PREVENT Blindness, New York, New York. The authors do not indicate any financial conflict of interest related to this study. Involved in design of the study (E.Y., L.W., D.D.K.); conduct of the study (E.Y., L.W., D.D.K.); collection, management, analysis, and interpretation of data (E.Y., L.W., D.D.K.); and preparation, review, or approval of the manuscript (E.Y., L.W., D.D.K.). This retrospective study was approved by the Institutional Review Board of Baylor College of Medicine, Houston, Texas.
REFERENCES 1. Huber C. Planned myopic astigmatism as a substitute for accommodation in pseudophakia. J Am Intraocul Implant Soc 1981;7(3):244 –249. 2. Nakazawa M, Ohtsuki K. Apparent accommodation in pseudophakic eyes after implantation of posterior chamber intraocular lenses. Am J Ophthalmol 1983;96(4):435– 438. 3. Nakazawa M, Ohtsuki K. Apparent accommodation in pseudophakic eyes after implantation of posterior chamber intraocular lenses: optical analysis. Invest Ophthalmol Vis Sci 1984;25(12):1458 –1460. 4. Fukuyama M, Oshika T, Amano S, Yoshitomi F. Relationship between apparent accomodation and corneal multifocality in pseudophakic eyes. Ophthalmology 1999;106(6): 1178 –1181. 5. Oshika T, Mimura T, Tanaka S, et al. Apparent accommodation and corneal wavefront aberration in pseudophakic eyes. Invest Ophthalmol Vis Sci 2002;43(9):2882–2886. 6. Nio YK, Jansonius NM, Wijdh RH, et al. Effect of methods of myopia correction on visual acuity, contrast sensitivity, and depth of focus. J Cataract Refract Surg 2003;29(11): 2082–2095. 7. Artola A, Patel S, Schimchak P, Ayala MJ, Ruiz-Moreno JM, Alió JL. Evidence for delayed presbyopia after photorefractive keratectomy for myopia. Ophthalmology 2006;113(5): 735–741.e1.
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8. Thibos LN, Applegate RA, Schwiegerling JT, et al. Standards for reporting the optical aberrations of eyes. In: MacRae SM, Krueger RR, Applegate RA, eds. Customized Corneal Ablation, the Quest for Supervision. Thorofare: Slack Inc, 2001:348 –361. 9. Dai GM. Optical surface optimization for the correction of presbyopia. Appl Opt 2006;45:4184 – 4195. 10. Applegate RA, Ballentine C, Gross H, Sarver EJ, Sarver CA. Visual acuity as a function of Zernike mode and level of root mean square error. Optom Vis Sci 2003;80(2):97–105. 11. Marcos S, Moreno E, Navarro R. The depth-of-field of the human eye from objective and subjective measurements. Vision Res 1999;39(12):2039 –2049. 12. Legge GE, Mullen KT, Woo GC, Campbell FW. Tolerance to visual defocus. J Opt Soc Am A 1987;4(5):851– 863. 13. Smolek MK, Klyce SD, Sarver EJ. Inattention to nonsuperimposable midline symmetry causes wavefront analysis error. Arch Ophthalmol 2002;120(4):439 – 447. 14. Marcos S, Barbero S, Jiménez-Alfaro I. Optical quality and depth-of-field of eyes implanted with spherical and aspheric intraocular lenses. J Refract Surg 2005;21(3):223– 235. 15. Rocha KM, Soriano ES, Chamon W, Chalita MR, Nosé W. Spherical aberration and depth of focus in eyes implanted with aspheric and spherical intraocular lenses: a prospective randomized study. Ophthalmology 2007;114(11):2050 – 2054.
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Biosketch Elizabeth Yeu received her Doctorate of Medicine through an accelerated undergraduate studies and medical school program from the University of Florida College of Medicine in 2003. She completed an ophthalmology residency at the Rush University Medical Center in Chicago, Illinois, where she served as the chief resident. Following residency training, Dr Yeu completed her fellowship in cornea, anterior segment and refractive surgery at the Cullen Eye Institute, Baylor College of Medicine, where she is currently an Assistant Professor in the Department of Ophthalmology. Her areas of interest reflect both the cornea and refractive surgery specialties, including advanced options in the treatment of keratoconus and innovations in cataract and refractive procedures. Dr Yeu currently serves on the Young Physicians Committee of the American Society of Cataract, the Ophthalmic News and Education Refractive subcommittee and the Refractive Surgery Annual Meeting subcommittee of the American Academy of Ophthalmology. She has authored several journal publications and book chapters, including monographs on astigmatism management, and novel lens implant options for cataract surgery.
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Biosketch Li Wang, MD, PhD, is a Assistant Professor at the Cullen Eye Institute, Department of Ophthalmology, Baylor College of Medicine. Her research interests are focused on cataract and refractive surgery.
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