figure 1. An example of an aspherical intraocular lens (AIOL) decentered 0.5 mm along the 180° meridian for a 6-mm pupil. The coefficient of fourth-order spherical aberration (Z40) in the AIOL is −0.29 μm, and the coefficient of the induced third-order horizontal coma (Z31) is −0.30 μm.
figure 2. Corneal higher-order aberrations (HOAs) and residual HOAs with centered and decentered aspherical intraocular lenses for a 6-mm pupil. Vertical bars indicate 2 SDs.
figure 3. Effect of aspherical intraocular lens decentration on the expected percentages of eyes that would meet the lower 10th percentile (P10) (A) and decreased higher-order aberration (DHOA) (B) criteria for the 4 pupil sizes.
figure 4. Effect of wavefront-corrected intraocular lens decentration on the expected percentages of eyes that would meet the. Marechal (MA) (A), lower 10th percentile (P10) (B), and decreased higher-order aberration (DHOA) (C) criteria for the 4 pupil sizes.
Wang L, Koch DD. Effect of Decentration of Wavefront-Corrected Intraocular Lenses on the Higher-Order Aberrations of the Eye. Arch Ophthalmol. 2005;123(9):1226-1230. doi:10.1001/archopht.123.9.1226
To evaluate the theoretical effect of decentration of aspherical intraocular lenses (IOLs) and wavefront-corrected IOLs up to the sixth order on higher-order aberrations (HOAs) (third through sixth order) of the eye.
An aspherical IOL with HOAs of fourth-order spherical aberrations only (−0.287 μm with a 6-mm pupil) and a wavefront-corrected IOL with HOAs of equal magnitude and opposite from the corneal HOAs were created and laterally shifted up to 1 mm to simulate decentered IOLs. The residual HOAs for pupils of 3 to 6 mm were calculated by combining the HOAs from the cornea and the decentered IOL. Based on the residual HOAs, optical quality was rated by 3 criteria: the Marechal criterion, a diffraction-limited optical system with an aberration less than λ/14; P10, the lower 10th percentile of the corneal HOAs in this study group; and decreased HOA, residual ocular HOAs less than the corresponding corneal HOAs.
Simulated implantation of the aspherical IOLs and wavefront-corrected IOLs was performed in 154 eyes of 94 patients aged 40 to 80 years. For a centered aspherical IOL and a 6-mm pupil, no eyes met the Marechal criterion, and the P10 and decreased-HOA criteria were met by 46% and 93% of eyes, respectively. For a 6-mm pupil, the required centration was 0.47 mm to meet the decreased-HOA criterion in 50% of eyes. With a wavefront-corrected IOL and a 6-mm pupil, the centrations required to meet the criteria for 90% of eyes were 0.04 mm for the Marechal criterion, 0.36 mm for P10, and 0.48 mm for the decreased-HOA criterion.
Excellent centration is required to maximize the visual outcome of wavefront-corrected IOLs.
With current surgical techniques, implantation of aspherical IOLs and wavefront-corrected IOLs will reduce total ocular HOAs below corneal HOAs in approximately 45% and 86% of eyes (6-mm pupil), respectively.
Aspherical or prolate intraocular lenses (AIOLs) have been used clinically to compensate for positive corneal spherical aberrations (SAs).1- 3 With emerging technology, wavefront-corrected intraocular lenses (WIOLs) will likely be introduced as a means of improving visual quality in pseudophakic eyes. An obvious concern about these wavefront-corrected lenses is the required accuracy of centration of the lens. Based on a model cornea derived from corneal elevation data in 71 eyes using Orbscan I topography (Bausch & Lomb, Rochester, NY), Holladay et al4 reported that the modulation transfer function of an eye with an AIOL would exceed that of the spherical IOL if the AIOL is decentered less than 0.4 mm.
Bueeler et al5 investigated the lateral alignment accuracy (ie, accuracy of centration) needed in wavefront-guided refractive surgery; they used 3 criteria of success based on the magnitude of residual ocular higher-order aberrations (HOAs). In this study, we apply these criteria to the theoretical effect of decentration of 2 types of wavefront-modified IOLs: an aspherical IOL and an IOL designed to correct all corneal HOAs (a WIOL).
The subjects were selected from our refractive-surgery candidates and cataract patients. Inclusion criteria were the following: (1) manifest refractive sphere of −3 to +3 diopters (D) and cylinder of less than 2 D; (2) age of 40 to 80 years; (3) no previous ocular or corneal surgery; (4) no corneal scar or other corneal pathology; (5) no contact-lens wear or contact lens wear discontinued for 8 weeks for rigid gas-permeable lenses, 4 weeks for toric soft lenses, and 2 weeks for soft lenses; and (6) no missing data points within the central 7-mm zone of Humphrey Atlas corneal topographic maps (Carl Zeiss, Inc, Pleasanton, Calif). A total of 154 eyes of 94 patients were included.
We created a surface with a fourth-order SA to represent the AIOL by using the CTView program (Sarver and Associates, Inc, Carbondale, Ill). The magnitude of SA incorporated in the AIOL was −0.287 μm, which was equal in magnitude but opposite in sign to the mean SA over the 6-mm zone in our sample.
We created a surface with HOAs (third to sixth order) with equal magnitude and opposite sign of the measured corneal HOAs to represent the WIOL for each cornea, using the CTView program.
Assuming implantation of the AIOL and WIOL in patients’ eyes, the combination of the wavefront aberrations from the AIOL (WAIOL) or WIOL (WWIOL) and from the patient’s cornea (WCOR) would produce the residual ocular aberration (WRES):
WRES = WCOR + WAIOL
WRES = WCOR + WWIOL
If the AIOL was perfectly centered, the WRES would equal the WCOR for all Zernike terms except the fourth-order SA, which would decrease or increase depending on the patient’s corneal SA. If the WIOL was perfectly centered, the WRES would be 0.
We computed WCOR from Humphrey Atlas corneal elevation data using the CTView program, which uses the standards for calculating and reporting the optical aberrations of eyes as proposed by Thibos et al.6 The topographic maps were recentered around the entrance pupil, and wavefront aberrations from the cornea were calculated using a corneal refractive index of 1.38.
Lateral shifts of the lens to 0.05, 0.10, 0.15, 0.20, 0.25, 0.50, 0.75, and 1.00 mm were performed to simulate a decentered AIOL or WIOL. We calculated WRES for eyes with centered and decentered lenses for 3-, 4-, 5-, and 6-mm pupils.
The root-mean-square (RMS) of WRES resulting from a decentered IOL was used to evaluate the optical quality of the eye and rated by 3 image-quality criteria as used in Bueeler et al’s study (Table 1)5:
Marechal (MA) criterion: The MA criterion states that a well-corrected, diffraction-limited optical system has an RMS wavefront error not exceeding λ/14. For a wavelength of 555 nm, the MA criterion was 0.04 μm. This strict criterion is difficult to achieve, especially in eyes with large pupils.
Lower 10th percentile (P10): The P10 criterion represents the lower 10th percentile of the preoperative corneal HOA (third- to sixth-order) RMS in the examined eyes. It was 0.06 μm for a 3-mm pupil and increased to 0.38 μm for a 6-mm pupil. If an eye meets this criterion, its optical quality is within the top 10% of this study group.
Decreased HOA (DHOA): This criterion is the least strict of the 3 and compares the residual aberrations with the corneal aberrations before surgery. The rationale of this criterion is that if an aberration-free IOL is implanted, the WRES would be caused only by the preexisting corneal aberrations, assuming that the corneal HOAs within the 6-mm zone do not change following the cataract incision. This criterion is fulfilled when the WRES is equal to or less than the corneal HOAs.
The required centration accuracies to meet the 3 criteria described herein 90% and 50% of eyes with the AIOL or WIOL were determined by the RMS of WRES as a function of the decentration of the IOL in millimeters (Δx):
RMS (WRES) = ƒ(Δx).
A second-order polynomial was used to fit the data. Decentration Δx, at which the corresponding criterion is violated, was obtained by intersecting the WRES for each eye with the rating criteria. For each of the 4 pupil sizes (3-6 mm), a set of 154 Δx for the 154 eyes included in this study was obtained for each criterion. The percentile values were then obtained for each set of Δx to represent the required centration accuracies to meet the criteria in 90% and 50% of eyes with AIOL or WIOL.
The mean ± SD age of the 154 eyes of 94 patients was 61 ± 12 years (range, 40-80 years). For a 6-mm pupil, the mean ± SD corneal total HOA was 0.51 ± 0.13 μm (range, 0.23-0.86 μm), and fourth-order SA was +0.29 ± 0.09 μm (range, 0.08-0.54 μm).
Coma was the main aberration induced by the decentered AIOL (Figure 1). figure 2 shows the WCOR and WRES with the centered and decentered AIOL for a 6-mm pupil. On average, the WRES was less than the WCOR if the AIOL was decentered less than 0.5 mm.
When the AIOL was perfectly centered, 1% of eyes met the MA criterion for the 3-mm pupil and none for the 4- to 6-mm pupils; 9%, 19%, 28%, and 46. of eyes met the P10 criterion (figure 3A); and 51%, 77%, 92%, and 93% of eyes met the DHOA criterion for 3-, 4-, 5-, and 6-mm pupils, respectively (figure 3B).
With increasing amounts of decentration, the percentages of eyes meeting the criteria decreased (figure 3). For 6-mm pupils, centration accuracies of 0.10 and 0.47 mm were required to meet the DHOA criterion in 90% and 50% of eyes, respectively (table 2).
figure 4 shows the percentages of eyes that met the MA, P10, and DHOA criteria at a specific decentration with the 4 pupil sizes. Decentration of less than 0.1 mm was required for most eyes to meet the MA criterion. A higher percentage of eyes met the MA criterion with smaller pupils at a specific decentration of the WIOL. For example, with a decentration of 0.1 mm, 69%, 57%, 21%, and 2% of eyes met the MA criterion for 3-, 4-, 5-, and 6-mm pupils, respectively (figure 4A).
Less critical centration was required to meet the P10 and DHOA criteria, and the alignment became less critical with larger pupils (figure 4B and C). For example, for 3-, 4-, 5-, and 6-mm pupils, and a decentration of 0.3 mm, 16%, 48%, 75%, and 92% of eyes met the P10 criterion, and 38%, 75%, 88%, and 98. of eyes met the DHOA criterion, respectively.
For 6-mm pupils, centration accuracies required to meet the MA, P10, and DHOA criteria in 90% of eyes were 0.04, 0.36, and 0.48 mm, respectively (table 3).
Clinical studies have shown that an aspherical IOL can improve visual performance, particularly contrast sensitivity and mesopic vision. An obvious concern of this lens is the effect of decentration on the optical outcome. Holladay et al4 reported that the modulation transfer function of an eye with an AIOL would exceed that of the spherical. IOL if the AIOL is decentered less than 0.4 mm or tilted less than 7°. The purpose of this study was to more fully explore the anticipated effect on ocular HOAs of decentration of an AIOL and to extend this investigation to WIOLs.
Because the AIOL compensates only for fourth-order SAs of the cornea, even with the perfectly centered lens, the ocular residual HOAs were 0.09 μm lower on average than the corneal HOAs. In the eyes measured in our study, it was not possible to meet the MA criterion with an AIOL, and only 9% to 46% of eyes met the P10 criterion with a perfectly centered AIOL. To ensure that 50% of eyes have ocular residual HOAs less than their corneal HOAs, the decentration could not exceed 0.27 mm for a 4-mm pupil or 0.37 mm for a 6-mm pupil. The allowed decentration of 0.47 mm is inconsistent with the findings of Holladay et al4 that the modulation transfer function for a 6-mm pupil would be improved if 20-D and 30-D AIOLs were not decentered more than 0.4 and 0.5 mm, respectively.
With a WIOL, the residual HOAs would be 0 if it is centered perfectly. To meet the MA criterion in 90% of the eyes, the lens has to be centered within 0.10 mm for a 3-mm pupil, and even more accurate centration is required as pupil size increases. To ensure that 90% of eyes have residual ocular HOAs within the P10 of normal corneal HOAs, WIOL decentration has to be less than 0.13 mm for a 3-mm pupil and 0.36 mm for a 6-mm pupil. If an aberration-free IOL is implanted, the residual ocular HOAs would be equal to the corneal HOAs. In the worst-case scenario, we probably do not want to induce more aberrations than the corneal HOAs. For ocular HOAs not to exceed corneal HOAs in 90% of eyes, our results show that the lens decentration has to be less than 0.20 mm for a 3-mm pupil and 0.48 mm for a 6-mm pupil.
In wavefront-guided corneal ablation, Bueeler et al5 reported that to achieve the diffraction-limited MA criterion in 95% of the eyes, lateral alignment accuracies of 0.21 and 0.07 mm or better were required for 3- and 7-mm pupils, respectively; to meet the P10 criterion, accuracies within 0.41 and 0.22 mm were required for 3- and 7-mm pupils, respectively. We found that more critical centration was required for the WIOL to meet the MA criterion and the alignment became less critical with larger pupils; this may be explained by the fact that corneal HOAs are larger than ocular HOAs, and corneal HOAs increase dramatically with increasing pupil size compared with ocular HOAs. In the study by Bueeler et al,5 a criterion of each eye’s total (second- to sixth-order) preoperative RMS wavefront aberration was used to rate the residual aberration; in contrast, we used the corneal HOAs of each eye.
What can surgeons expect with regard to the accuracy of IOL centration. With continuous curvilinear capsulorrhexis and in-the-bag IOL placement, mean IOL centration has been reported to be within 0.1 to 0.3 mm.7- 9 referring to table 1, we see that with a 6.0-mm pupil and decentration of 0.47 mm, 50% of eyes will experience a reduction in the HOAs compared with HOAs that are present in their corneas. One can therefore conclude that less than half of all patients implanted with AIOLs will have postoperative ocular HOAs that are lower than the HOAs in their corneas. With regard to WIOLs (Table 3) with a 6.0-mm pupil and a decentration of 0.48 mm, total ocular HOAs were less than those present in the cornea in 90% of eyes. One can therefore conclude that the majority of eyes implanted with WIOLs will experience postoperative HOAs that are less than those present in the cornea preoperatively. Obviously, clinical evaluation is required to determine the visual impact of these changes on patients’ quality of vision.
A major limitation of this study is that the RMS of the residual wavefront aberration was used as a representation of the optical quality of the eye. Although reports show a significant but weak correlation between determined RMS values and high- and low-contrast visual acuity,10,11 Applegate et al12 reported that different Zernike terms with the equivalent RMS values can interact to improve or reduce visual performance. Further studies are required to define parameters that correlate well with visual performance.
Other limitations of this study include that it is a theoretical analysis, clinical studies investigating the required alignment of the lens based on visual performance are obviously required, and we did not model the effect of torsional misalignment of the IOL on the change in ocular HOAs.
In conclusion, our results demonstrate that excellent centration is required to maximize the reduction of HOAs following implantation of wavefront-modified IOLs.
Correspondence: Douglas D. Koch, MD, Department of Ophthalmology, Baylor College of Medicine, 6565 Fannin, NC205, Houston, TX 77030 (firstname.lastname@example.org).
Submitted for Publication: October 7, 2004; final revision received February 7, 2005; accepted February 8, 2005.
Financial Disclosure: None.