It is known that laser-assisted in situ keratomileusis (LASIK) modifies higher-order aberrations.1–7 Changes in higher-order aberrations after corneal refractive surgery have been reported using either corneal front surface aberrations derived from corneal topography1 or whole-eye ocular aberrations measured directly with aberrometers.2,3
In LASIK, because higher-order aberrations are induced on the cornea, it is logical to use a topographic system that directly measures the corneal surface to derive corneal higher-order aberrations and characterize the change in higher-order aberrations induced by LASIK. One advantage of this technique is that corneal aberrations can be calculated for a large diameter independently of the pupil size, which suppresses the need for pupil dilation.
Another technique to quantify the change in higher-order aberrations after LASIK is to use whole-eye ocular aberrations measured with aberrometers. One advantage of this technique is that whole-eye ocular aberrations represent the total amount of aberrations of the optical system of the eye, including internal aberrations, and should therefore be better correlated to visual quality measurements and/or any visual symptoms. One disadvantage is that pupil dilation is often required.
Each of these techniques uses a different calculation reference point as center of the wavefront measurement: corneal wavefront aberrations are measured with reference to the corneal vertex whereas ocular wavefront aberrations are—by convention—measured with reference to the entrance pupil center.8 This implies that in eyes with a large angle kappa (where the location of the corneal vertex is different to the location of the entrance pupil center), corneal aberrations are being measured from a different reference point and therefore cannot be directly subtracted from whole-eye aberrations to derive internal aberrations. In eyes with a very small angle kappa, the locations of the corneal vertex and the entrance pupil center are similar. Therefore, for eyes with small angle kappa, the change in aberrations induced by LASIK should be similar if measured on the corneal front surface alone or as a change in whole-eye aberrations.
In clinical practice, refractive surgeons use both technologies. Therefore, the aim of our study was to investigate whether corneal aberrometry and whole-eye aberrometry were interchangeable by comparing the change in higher-order aberrations induced by LASIK.
This study was a retrospective case series from consecutive patients treated with LASIK at the London Vision Clinic, London, UK. All treatments were performed as bilateral simultaneous LASIK by a highly experienced single surgeon (DZR). All subjects gave their informed consent for the use of their data for research, analysis, and publication purposes.
Inclusion criteria were as follows: age between 18 and 50 years, corrected distance visual acuity 20/20 or better, myopic spherical equivalent refraction less than or equal to −0.75 diopters or hyperopic spherical equivalent greater than or equal to +0.38 diopters, available preoperative and at least 3 months postoperative corneal topography and aberrometry data, available preoperative Orbscan II tomography (Bausch and Lomb Inc, Salt Lake City, UT), and pupil offset less than or equal to 0.25 mm. Pupil offset was defined as the distance in the corneal plane between the entrance pupil center and the corneal vertex, as measured directly on the Eye Image of the Orbscan II. Only eyes with a small pupil offset (<0.25 mm) were selected to limit the difference in location between the entrance pupil center and corneal vertex and therefore allow direct comparison between corneal front surface aberrations and whole-eye aberrations.
A sample size calculation to obtain a power of 0.95 assuming an SD of 0.15 μm and a minimum change of 0.075 μm determined that we required at least 48 eyes to be included for study.
Consecutive eyes fulfilling all inclusion criteria were selected until the number of eyes in the hyperopic group reached 50 and that of the myopic group reached 100.
A full ophthalmologic examination was performed on all patients before surgery including manifest refraction, corneal front surface topography using the Atlas 999 (Carl Zeiss Meditec, Jena, Germany), and whole-eye wavefront assessment using the WASCA aberrometer (Wavefront Aberration-Supported Corneal Ablation; Carl Zeiss Meditec). Atlas topography and WASCA aberrometry were also obtained 3 months postoperatively.
All patients underwent LASIK using the MEL80 (Carl Zeiss Meditec) excimer laser. A nonlinear aspheric ablation profile was used in all eyes, which is now commercially available as part of the Laser Blended Vision module for the CRS-Master.9 All myopic eyes were treated with the z16 head Hansatome zero-compression microkeratome (Bausch & Lomb, St. Louis, MO) and the 160-μm head, with a mean (±SD) ablation zone of 6.01 (±0.10) mm (range, 5.75 to 6.50 mm). For hyperopic eyes, 25 eyes were treated with the z16 head Hansatome zero-compression microkeratome, 1 eye was treated with the z18 Hansatome zero-compression microkeratome, and 24 eyes were treated with the VisuMax femtosecond laser (Carl Zeiss Meditec) with a mean (±SD) flap thickness of 118.4 (±10.8) μm (range, 98 to 138 μm). The mean (±SD) hyperopic ablation zone was 6.87 (±0.24) mm (range, 6.00 to 7.00 mm).
All excimer ablations were centered on the coaxially sighted corneal light reflex (CSCLR). During surgery, the CSCLR was determined, before the flap was lifted, as the first Purkinje reflex with the patient fixating coaxially to the surgeon viewing through the contralateral eye of the operating microscope. The CSCLR was used as the best approximation of the intersection of the visual axis with the cornea.10
The Atlas Review Software version 188.8.131.52 (Carl Zeiss Meditec) was used to calculate the corneal front surface wavefront aberrations derived from Placido topography acquired before and at least 3 months after surgery. Corneal front surface wavefront aberrations were calculated based on the corneal vertex as reference center. Whole-eye ocular aberrations were measured directly with the WASCA aberrometer (centered with reference to the entrance pupil center). Both corneal and whole-eye ocular higher-order aberrations were described by Zernike polynomials up to the fourth order and were calculated for a 6-mm analysis zone using the OSA (Optical Society of America) convention for notation.
Repeatability of the WASCA aberrometer has been previously reported by Salmon and van de Pol.11 There are no published studies on the repeatability of the Atlas 9000 for corneal front surface aberrations; thus, a substudy was carried out on a sample of 10 low myopic patients. Repeatability of the Atlas 9000 for corneal front surface aberrations was calculated using the method described by Salmon and van de Pol so that the repeatability of both instruments could be compared. One eye of each patient was randomly selected and scanned four times. From the four measurements, we computed the SD, SE, and 95% confidence interval. The confidence intervals were averaged across the 10 eyes. The repeatability was calculated for the following parameters: third-order root mean square (RMS) and fourth-order RMS.
Student paired t test was used to compare the change in aberrations measured by either corneal front surface aberrometry or whole-eye aberrometry. The following parameters were analyzed: all individual Zernike coefficients from the second order to the fourth order, total higher-order RMS (HORMS) from the third up to the fourth order, third-order RMS (RMS of all third-order coefficients), fourth-order RMS (RMS of all fourth-order coefficients), and RMS coma (RMS combination of Z3−1 and Z3+1). A Bonferroni correction was applied to account for multiple comparisons of all 12 Zernike coefficients. Therefore, a p value of 0.04 (=0.05/12) was required to reach statistical significance. The correlation between corneal aberrometry and whole-eye aberrometry was plotted for the following parameters: HORMS, spherical aberration (Z40), vertical coma (Z3−1), and horizontal coma (Z3+1). Linear regression was performed and Pearson correlation coefficient (r2) was calculated. All statistical analysis was performed in Excel 2007 (Microsoft, Redmond, WA).
The population demographics are reported in Table 1 for both groups.
The repeatability of WASCA and Atlas measurements were comparable as presented in Table 2.
Change in Aberrations
Box plots of aberrometry before and after LASIK for corneal front surface aberrometry and whole-eye ocular aberrometry for myopic eyes are shown in Fig. 1 and those for hyperopic eyes are shown in Fig. 2. The change in aberrations induced by myopic LASIK for corneal front surface aberrometry and whole-eye ocular aberrometry is reported in Table 3 and that induced by hyperopic LASIK is shown in Table 4. The correlation between corneal front surface aberrometry and whole-eye aberrometry for HORMS and spherical aberration is shown in Fig. 3 and that for vertical and horizontal coma is shown in Fig. 4.
For myopic eyes, the magnitude of change in higher-order aberrations (HORMS), defocus (Z20), secondary astigmatism (Z4−2), and spherical aberration (Z40) was statistically significantly different (p ≤ 0.004) when measured by front surface corneal aberrometry alone or whole-eye aberrometry. The change detected in whole-eye HORMS was statistically significantly lower for whole-eye aberrometry (0.230 μm) than for corneal aberrometry (0.307 μm). This is explained by the slopes of the regression lines shown in Fig. 3. The induction of HORMS was 66% lower for whole-eye aberrometry than for corneal aberrometry. Fig. 3 also shows that the induction of vertical coma was 54% lower for whole-eye aberrometry than for corneal aberrometry and that the induction of horizontal coma was 38% lower for whole-eye aberrometry than for corneal aberrometry. However, the change detected in coma coefficients (Z3−1 and Z3+1) was not statistically significantly different when measured by corneal aberrometry and whole-eye aberrometry. On the other hand, the change detected in whole-eye spherical aberration (0.308 μm) was statistically significantly greater than the change detected in corneal spherical aberration (0.243 μm). As shown in Fig. 3, although the slope of the regression was close to 1 (1.038), whole-eye spherical aberration was measured as greater than corneal spherical aberration by 0.056 μm on average.
For hyperopic eyes, the magnitude of change in higher-order aberrations (HORMS) and defocus (Z20) was statistically significantly different (p < 0.004) when measured by front surface corneal aberrations alone or whole-eye aberrometry. The change detected in HORMS was statistically significantly lower for corneal aberrometry (0.164 μm) than for whole-eye aberrometry (0.259 μm). Fig. 4 shows that although the induction of vertical coma was 56% lower for whole-eye aberrometry than for corneal aberrometry, horizontal coma and spherical aberration increased at almost the same rate for both whole-eye aberrometry and corneal aberrometry.
This study demonstrated that when measuring the change in higher-order aberrations induced by LASIK, corneal front surface aberrometry measurement was not interchangeable with whole-eye ocular aberrometry.
In this study, two different technologies were used to measure higher-order aberrations induced by LASIK. Corneal topography was used to measure front surface corneal aberrations and Hartmann-Shack aberrometer was used to measure whole-eye aberrations. Although several systems now exist where one platform is used to measure both front surface corneal aberrations and whole-eye ocular aberrations, the measurements are still made with different technologies, that is, Placido topography and Hartmann-Shack aberrometry. Because most, if not all, refractive surgeons use both corneal topography and aberrometry to diagnose abnormalities, plan surgery, and assess patient postoperatively, it is important to understand whether measurements obtained from both technologies are directly comparable or not.
To make the comparison between front surface corneal aberrometry and whole-eye aberrometry possible, it was necessary to make sure that the reference center used for the wavefront calculation was similar between corneal and whole-eye wavefront measurements. Hence, all eyes were specifically selected so that the pupil offset defined as the distance in the corneal plane between the corneal vertex and the entrance pupil center was small (less than 0.25 mm), and therefore the locations of the corneal vertex (reference center for corneal wavefront measurement) and the entrance pupil center (reference center for ocular wavefront measurement) were similar. Given that previously published studies comparing front surface corneal aberrations and ocular aberrations did not include any restriction on pupil offset values, limiting the value to 0.25 mm in our study provides the ability to directly compare corneal to whole-eye aberrations by minimizing the error that may be induced by the difference in calculation center between the two techniques. The value of 0.25 mm was deliberately chosen based on the distribution of the pupil offset in normal population of myopes and hyperopes, in which the mean (±SD) pupil offset was 0.27 (±0.14) mm (range, 0.00 to 0.68) in myopic eyes and 0.40 (±0.13) mm (range, 0.21 to 0.72) in hyperopic eyes.12 The cutoff value of 0.25 mm allowed for 53% of all myopic eyes and for 13% of all hyperopic eyes to be included. Although a smaller value of pupil offset may have been better to compare corneal aberrations and ocular aberrations, it would have made it very difficult to recruit enough hyperopic eyes. Although we cannot exclude the possibility that some differences in the magnitude of the change in aberrations between the two techniques could be accounted for by different centration of calculations to derive the higher-order Zernike coefficients, it is certainly unlikely that it is responsible for the large differences that were observed in this study. The corollary is that it would be expected that for eyes with a large pupil offset, the difference between front surface corneal wavefront and ocular wavefront would be larger.
In myopic eyes, the magnitude of change in higher-order aberrations induced by LASIK measured with the WASCA aberrometer was smaller than the magnitude of corneal front surface aberrations derived from topography. This is in agreement with previous papers where corneal and ocular aberrations induced by corneal refractive surgery were compared. All studies demonstrated that the induction of corneal aberrations was always at least the same as13,14 or higher than7,15,16 the induction of whole-eye ocular wavefront aberrations. AlMahmoud et al.7 reported that ocular wavefront aberrations after refractive surgery were smaller than corneal aberrations. Arba Mosquera and de Ortueta15 reported that, in myopic eyes, corneal and ocular spherical aberration were correlated in a statistically significant manner, with ocular spherical aberration increasing at a rate of half of the corneal spherical aberration. Marcos16 found that after myopic LASIK, ocular aberrations increased by an average factor of 1.92 and corneal aberrations increased by an average factor of 3.72. In our study, corneal and ocular spherical aberrations were also statistically significantly correlated, and postoperatively, ocular spherical aberration was smaller than corneal spherical aberration; however, the induction of ocular spherical aberration was greater than the induction of corneal spherical aberration. Interestingly, in our study, coma showed the largest difference when measured with both techniques; whole-eye coma increased at less than half the rate of corneal coma.
In hyperopic eyes, the magnitude of change in higher-order aberrations induced by LASIK measured with the WASCA aberrometer was larger than the magnitude of corneal front surface aberrations derived from topography. However, there was no statistically significant difference for individual Zernike coefficients. This could be explained by the fact that the data were more scattered in the hyperopic group as shown by larger SD values of aberration parameters measured and also by the fact that the number of eyes in the hyperopic group was smaller. Therefore, a larger difference between the two measurement techniques would be required to be statistically significant. The correlation plots demonstrated that spherical aberration and horizontal coma increased at the same rate when measured with either corneal aberrations or whole-eye aberrations, in contrast to myopic eyes. To the best of our knowledge, no other study has reported the correlation between the change in corneal aberrations and the change in ocular aberrations in post-LASIK hyperopic eyes. Further study on a larger sample of eyes might be required to confirm our findings.
In both myopic and hyperopic groups, spherical aberration demonstrated the greatest change out of all third- and fourth-order Zernike coefficients. This is because spherical aberration was always induced in the same direction in all eyes; that is, myopic LASIK induces positive spherical aberration, whereas hyperopic LASIK induces negative spherical aberration. In contrast, other Zernike coefficients became either more positive or more negative for individual eyes after LASIK. It should be noted that the change in spherical aberration as reported in Tables 3 and 4 was larger than the change in HORMS. This can be explained by the fact that the average change in HORMS was obtained by first calculating the individual HORMS before and after surgery, then the individual change in HORMS, and finally the average change across all eyes. If the change in HORMS had been obtained by first calculating the change in individual Zernike coefficient between before and after surgery and then calculating the RMS based on the change in individual Zernike coefficients, the change in HORMS would have been much greater and always greater than any individual Zernike value. However, we chose the calculation method as this represents how clinicians calculate the amount of aberrations induced.
The difference in the amount of aberrations induced between front surface corneal wavefront measurement and ocular wavefront measurement might be partly explained by the difference in the measurement principle. Corneal front surface aberrations are calculated based on the elevation data obtained from the corneal topography. Calculations are based on the assumption of an ideal corneal single thin lens. On the other hand, ocular aberrations are measured directly using a wavefront sensor that analyzes the light reflected back from the retina after passing through the optical system of the eye. For Hartmann-Shack aberrometers, the accuracy of the measurement depends mainly on the resolution of the Hartmann-Shack screen (i.e., the number of lenslets). Recently, Fabrikant and Chernyak17 provided an explanation for the difference between the measurements obtained with both techniques. The authors presented a mathematical method to recalculate wavefront aberration and corneal aberration changes induced by LASIK; first, each wavefront measurement was recalculated so that it is aligned with the corneal vertex, thus eliminating the pupil offset error. Then, a correction factor for the change in light propagation path after corneal tissue ablation was included. The authors demonstrated that a strong correlation between both measurement techniques could be obtained once these corrections have been applied and concluded that changes in aberrations could not be simply computed as the difference between preoperative and postoperative measurements.
The difference between corneal aberrations and whole-eye aberrations could be attributed to some changes in internal aberrations and in particular changes occurring in the posterior corneal surface. Lee et al.18 demonstrated a forward shift of the posterior corneal surface of 24.3 ± 9.76 μm after LASIK. These changes might account for some of the difference between induced corneal front surface wavefront and ocular wavefront.
In conclusion, this article demonstrated that corneal front surface aberration measurements derived from topography and whole-eye ocular aberration measurements obtained from aberrometry were not interchangeable to assess the amount of aberrations induced by LASIK. Measuring the change in corneal front surface aberrations is useful to assess how higher-order aberrations are modified after refractive surgery procedures, in particular if the surgery was centered on the corneal vertex. Total ocular wavefront measured by aberrometry can be useful to evaluate the total amount of aberrations in the optical system of the eye after surgery and correlate the aberrations with visual symptoms. However, some error in this correlation will be induced if corneal ablation was centered on the corneal vertex and the wavefront aberrations were measured with reference to the entrance pupil center. It is essential to remember that both methods of aberration measurement use a different reference point for the center of the wavefront: the corneal vertex for corneal aberrations and the entrance pupil center for ocular wavefront.
London Vision Clinic
138 Harley St
London W1G 7LA
Dr. Reinstein is a consultant for Carl Zeiss Meditec (Jena, Germany), has a proprietary interest in the Artemis technology (ArcScan Inc, Morrison, CO), and is an author of patents related to VHF digital ultrasound administered by the Cornell Research Foundation, Ithaca, NY. The remaining authors have no proprietary or financial interest in the materials presented herein.
Received July 16, 2014; accepted February 6, 2015.
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