New ablation profiles have been developed and integrated in the new generations of excimer lasers with the aim of treating not only lower order aberration but also higher order aberration (HOA) wavefront errors.1 However, controversy remains concerning the need for treating all preexisting HOAs to reach the best visual quality.2,3 The wavefront-optimized profile was designed to compensate for the spherical aberrations of the total eye induced by standard treatment while preserving the preexisting optical aberrations of the eye.4 Because most wavefront systems assess the wavefront pattern of the whole eye, few studies have investigated the effect of these new ablation profiles on corneal wavefront errors. The corneal wavefront profile does not reflect the visual performance; however, it provides information about the optical response of the cornea to these ablation profiles, which may help in optimizing new laser treatment algorithms.
In this study, we evaluated corneal HOAs induced by different levels of myopic correction after wavefront-optimized ablation. The objective was to analyze whether the wavefront-optimized profile successfully and evenly preserved the preexisting corneal aberrations and eccentricity of the cornea for different levels of attempted myopic correction.
Patients and Methods
This prospective comparative study was performed at the Cole Eye Institute, Cleveland, Ohio, approved by the Cleve-land Clinic’s Institutional Review Board, and conducted in accordance with the tenets of the Declaration of Helsinki.
Patients with myopia or myopia with astigmatism were prospectively enrolled from February to July 2011, when they met previously published standard criteria for LASIK after a screening evaluation.5 Patients with previous ocular surgery or candidates for hyperopic treatment were not included in this study. Eyes were divided into 3 groups based on the spherical equivalent (SE) of the intended correction ranging from −0.13 to −9.25 diopters (D). The low myopia group included patients with SE <−3.00 D, the moderate myopia group included patients with SE between −3.00 and −6.00 D, and the high myopia group included patients with SE >−6.00 D.
All patients had a detailed preoperative ophthalmic evaluation including uncorrected (UDVA) and corrected distance visual acuity (CDVA) using Early Treatment Diabetic Retinopathy Study (ETDRS) charts, manifest and cycloplegic refraction, slit-lamp evaluation, applanation tonometry, and fundus examination. All eyes were imaged preoperatively and 3 months after surgery with the dual-Scheimpflug imaging system (Galilei analyzer; Ziemer Ophthalmic Systems AG, Port, Switzerland).
All surgeries were performed by a single experienced surgeon (R.K.) with a wavefront-optimized photoablation profile using the WaveLight Allegretto Wave Eye-Q (400-Hz; Alcon Laboratories Inc, Ft Worth, Texas) excimer laser. Laser in situ keratomileusis procedures were performed with a 0.95-mm spot size, an optical zone of 6.25 mm, and a transition zone of 1.25 mm.
The magnitude of the spherical and astigmatic correction was first determined using software nomogram suggestions from clinical refractive measurements that were entered in the SurgiVision DataLink Alcon Edition (SurgiVision Inc, Scottsdale, Arizona) and adjustments were made by the surgeon based on final assessment of all available clinical data.
The WaveLight FS200 femtosecond laser (Alcon Laboratories Inc) was used to create an intended 100-μm–thick corneal flap with a superior hinge. Postoperatively, Vigamox ophthalmic solution (Alcon Laboratories Inc) and prednisolone acetate 1% ophthalmic solution (Alcon Laboratories Inc) were applied four times daily for 1 week.
Dual Scheimpflug Imaging
Measurements were performed with the Galilei dual Scheimpflug analyzer system (software version 5.2.1) according to the manufacturer’s guidelines. Only measurements that satisfy the minimum quality required by the system were included in this study.
The eccentricity of the cornea (ε2), the total corneal HOA RMS from the 3rd to 6th order, RMS spherical aberration Z(4,0), and RMS coma (this value is calculated from the vertical Z[3,−1] and horizontal Z[3,1] coma) through a 6-mm pupil size were recorded. Eccentricity (ε2) is one of the four parameters by which the shape of a conic section can be described; Q (asphericity), P value, and E (corneal shape factor) are the others. These terms are mathematically related by the following equation: ε2 = E = 1 − p = −Q. The eccentricity is calculated within a central diameter of 8 mm averaged over all meridians of the anterior corneal surface. A positive value refers to a prolate shape of the corneal surface whereas a negative value refers to an oblate shape.
Correlations between the intended spherical equivalent of the correction (SEc) and the achieved ablation depth with the induced total RMS corneal HOAs, RMS corneal spherical aberration, RMS corneal coma, and corneal eccentricity were tested. The induced RMS corneal aberrations (Δ RMS) were calculated as the difference of the RMS values before and after surgery. In addition, correlations between the SEc and the induced RMS spherical aberration with the total corneal power in the midperiphery (TCPmid) were also tested. The midperiphery is defined by the area located between 4 and 7 mm and therefore includes a part of the transition zone, which is thought to be responsible for the induction of spherical aberrations after myopic laser treatment. In addition, the TCP provides information on the real corneal power with which the incoming rays of light will be refracted, unlike the keratometric power that gives information on corneal curvature at a focal point.
The TCP, which is calculated by the Galilei system, is the actual power of the cornea including both the anterior and posterior surfaces. The TCP power and map are calculated by tracking the path of incident rays of light through the three-dimensional cornea using ray tracing. Ray tracing is a method of modeling the power of a lens by tracing incident parallel rays of light through an optical system, such as the cornea. This method uses Snell Law to refract the incoming rays of light and considers the three-dimensional shape of the cornea and the difference in indices of refraction at each surface, which affects how the rays of light are bent. The three-dimensional corneal shape is defined by the anterior surface curvature, corneal thickness (pachymetry), and posterior surface curvature, whereas the index of refractions used are n=1.0 for air, n=1.376 for cornea, and n=1.336 for aqueous. Corneal power is then determined by n/f where f is the focal length, referenced to the anterior corneal surface, and n the index of refraction of the aqueous (n=1.336). We recorded the average TCP over the midperipheral zone (4 to 7 mm) before and 3 months after surgery and tested the correlations with the amount of intended correction and induced spherical aberration over a 6-mm pupil size.
Statistical analyses were performed using JMP software (version 8.0; SAS Institute Inc, Cary, North Carolina). Normality of data was investigated with the Kolmogorov-Smirnov test. Differences between data were evaluated using the Wilcoxon test or analysis of variance (ANOVA), whereas correlation coefficients were established by Spearman rank correlation. Data were expressed as mean and standard deviation. The level of significance for each parameter was set at P<.05. A portion of the statistical analyses concerned the question of dependence between observations. Because for most patients the data included both eyes, it seemed plausible that intraclass correlation would exist within a patient; therefore, the whole database could not be considered as independent observations. We initially used the mixed model for comparing groups because the mixed model takes into account the dependence among observations. However, results of this analysis indicated that there was no dependence, therefore the independence assumption was valid.
This study included 64 myopic eyes from 36 patients; 30 eyes were in women (47%). Baseline clinical and demographic characteristics of the patients by groups are summarized in Table 1. In this study population, the high myopia group had a significantly smaller amount of preoperative RMS spherical aberrations. However, these values were not used in our analysis because the amount of correction for induced spherical aberration is proportional to the treated spherical equivalent and is independent of the preoperative corneal wavefront measurement.
Table 1: Baseline Clinical Characteristics and Demographics of Eyes That Underwent Wavefront-optimized Myopic LASIK
Changes in Corneal HOA
Postoperative changes for each analyzed parameter are summarized by refractive status in Table 2.
Table 2: Changes in Corneal Higher Order Aberrations From Baseline to 3 Months After LASIK
Although a statistically significant increase in total corneal HOA was noted overall, it was statistically significant only after treatment for moderate and high myopia. The Zernike coefficient that varied the most after myopic ablation was RMS spherical aberration Z(4,0). This induction was only statistically significant for the moderate and high myopic treatments. The induction of spherical aberration after treatment for low myopia was nearly zero and not statistically significant. The change in RMS coma was statistically significant only in the high myopia group.
An overall decrease in eccentricity was observed in all groups after myopic ablation, although it was statistically significant only in the moderate and high myopia groups. This decrease in eccentricity after myopic ablation translates into an expected shift of the cornea towards a more oblate shape.
The postoperative increase factors for each corneal RMS aberration, defined as the ratio between the RMS values after and before LASIK, are shown in Table A (available as supplemental material in the PDF version of this article).
Correlations Between Parameters
The amounts of induced corneal spherical aberration as well as the magnitude of change in eccentricity are correlated with the SE (Table B, available as supplemental material in the PDF version of this article). The correlations between the magnitude of the myopic treatment with the amount of induced spherical aberrations and the change in eccentricity are shown in Figure 1. The higher the myopic correction achieved, the higher the induction of positive corneal spherical aberration and the greater the decrease in eccentricity. The change in eccentricity is also highly correlated with the amount of induced spherical aberration (SC=0.97; P<.001). The greater the decrease in eccentricity (shift toward oblateness), the greater the induction of positive corneal spherical aberration.
Figure 1. Scatterplots showing the correlation between A) the postoperative induction of spherical aberration (SA) and B) the change in eccentricity with the spherical equivalent of the achieved myopic correction.
Correlations between the amount of induced spherical aberration and the magnitude of the myopic correction with the corneal power in the midperiphery were high (Spearman coefficient 0.81, P<.0001; and Spearman coefficient 0.92, P<.0001, respectively) and are shown in Figure 2. Results of these correlations are shown in Tables B and C (available as supplemental material in the PDF version of this article).
Figure 2. Scatterplots showing the correlation between the postoperative increase in total corneal power in the midperiphery (4 to 7 mm) with A) the amount of induced spherical aberration and B) magnitude of the achieved myopic correction. SA = spherical aberration, TCP = total corneal power, SE = spherical equivalent
Mrochen et al4 incorporated compensation for the cosine effect by increasing the laser fluence in the periphery and compensation for the amount of surgically induced spherical aberration into a nomogram, which is the fundamental mathematical basis behind the wavefront-optimized profile, for calculating the amount of the required compensation.
In the present study, our results suggest that the use of the wavefront-optimized profile still induces corneal spherical aberrations and fails to maintain the preoperative corneal eccentricity in moderate and high myopic corrections. In addition, we found that the amount of spherical aberration induction as well as the magnitude of change in corneal eccentricity is highly correlated to the level of achieved myopic correction.
Our results are similar to those already reported in the literature with conventional myopic ablation. Although in the present study we report an overall increase in corneal HOA, spherical aberrations, and coma through a 6-mm pupil by a factor of 1.39, 3.16, and 1.36, respectively, Oshika et al6 reported a significant increase in corneal spherical aberration and coma-like aberrations after surgery by a factor of 9.4 and 4.4, respectively, through a 6-mm pupil after conventional ablation. This increase in corneal HOAs was significantly correlated to the amount of refractive correction. More recently, Gatinel et al,7 reported an overall postoperative increase in corneal HOAs by a factor of 2.47 with an increase in corneal spherical aberration and corneal coma by a factor of 2.64 and 2.56, respectively. Bottos et al8 reported a similar postoperative increase in corneal spherical aberration through a 6-mm pupil and a significant change in corneal asphericity among a large series of wavefront-guided myopic LASIK. The amount of induced aberrations was significantly related to the magnitude of the preoperative refractive error. The authors reported an increase of +0.04 μm in corneal spherical aberration for each diopter of myopic ablation and a mean asphericity change of +0.63 in the direction of a more oblate corneal shape. In our study, we found a mean eccentricity change of −0.67 (eccentricity ε2 = −Q) and an increase of +0.10 μm in corneal spherical aberration for each diopter of myopic ablation and through a 6-mm pupil (see Fig 1A). The postoperative change in eccentricity and corneal spherical aberration was statistically significant only after moderate and high myopic corrections. However, we found a significant postoperative increase in corneal coma only in the high myopic group. Kamiya et al9 retrospectively analyzed the factors influencing the changes in coma-like aberrations after LASIK and showed that high myopic corrections tended to induce more coma because of longer ablation time and higher risk of decentration. This might be a reasonable explanation for the higher induction of coma found in the high myopic group as well as the larger standard deviation found with higher myopic corrections. The relatively small sample size of patients in this group may also be in part responsible for the larger standard deviation.
This is the first study to analyze in vivo the induction of corneal HOAs after wavefront-optimized ablation. The wavefront-optimized profile has been designed to compensate for the spherical aberration of the total eye induced with the conventional treatment, preserving the preexisting optical aberration of the eye. Induction of positive spherical aberration after myopic LASIK has been extensively studied and mainly attributed to physical effects rather than biological effects (biomechanical and wound healing) as shown in experimental studies on a polymethylmethacrylate (PMMA) model.10–12
Aspheric profiles have been developed considering the loss in ablation efficacy in the periphery and compensate for that by increasing the pulse energy in this area. However, in a recent experimental study on a PMMA model, although the authors showed optical benefits of aspheric ablations over standard ablations with significantly less induction of spherical aberration and better retinal image quality, a profound induction of spherical aberration remained with the aspheric profile after an ablation of −6.00 D with a 6-mm optical zone.12 As the PMMA model ensured a treatment effect free of biological responses, the authors concluded that the induction of positive spherical aberration was due to loss of laser ablation efficiency in the lens periphery (laser fluence loss toward the peripheral cornea), which is also known as the so-called “cosine effect.”
This hypothesis concurs with our present finding, showing a significant postoperative increase in corneal power in the midperiphery (TCP), which might reasonably be related to a loss in ablation efficiency in the paracentral cornea. Along the same corneal meridian, an area with a higher optical power will refract more the incoming rays of light, resulting in a different plane of focus. When this area of higher optical power is located in the periphery with a lower optical power in the center, the incoming rays of light passing through the cornea will be refracted in such a way that it will induce positive spherical aberration. This optical effect explains the strong correlation between the postoperative induction of positive spherical aberration with the increase in corneal TCP in the midperiphery (4 to 7 mm), which includes a part of the transition zone.
In a recent study by our group, which analyzed the postoperative induction of total ocular HOA 3 months after wavefront-optimized LASIK, we found different results with no significant increase in HOA after surgery and no correlation between the postoperative spherical aberration induction and magnitude of the corrected myopia.13 The induced spherical aberrations of the total eye were −0.024 (P=.09), 0.008 (P=.52), and −0.020 (P=.35) after treatment for low, moderate, and high myopia, respectively. However, in the present study, we analyzed the variations of the corneal HOAs after surgery, which more closely reflect the response of the cornea to an aspheric ablation. It has been already shown that the magnitude of the corneal HOA individually is larger than for the whole eye due to the internal compensation of the corneal aberrations.14,15
Gatinel et al7 analyzed the aberration compensation mechanism after sudden optical decoupling of corneal and lenticular HOAs due to myopic LASIK. The authors found that, although there was a significant induction of corneal HOA (increase by a factor of 2.47), which was larger than the total ocular HOA (increase by a factor of 1.77), the level of partial compensation of corneal aberrations remained unchanged after surgery due to a proportional increase in internal aberrations compensation. They suggested, based on ray tracing analysis, that due to the surgically induced change in anterior corneal shape, the light rays emerging from the posterior surface struck the lens in such a way that modified the lenticular aberrations and maintained the same level of internal aberrations compensation postoperatively. This finding was supported by another recent study, showing that corneal spherical aberration increased after LASIK with a corresponding increase in the internal spherical aberration, translating an active compensatory mechanism of the internal optics to reduce the effect of the surgically induced corneal HOA.16
This hypothesis may be one explanation for the discrepancy between the results of our present study showing an increase in corneal spherical aberration after wavefront-optimized ablation and our former study that showed no induction in total ocular spherical aberration after using the same ablation profile. However, it has to be noted that in the above-cited studies, total ocular aberrations were not measured under cycloplegia; therefore, it cannot be ruled out that the accommodation response played a significant role in the compensatory mechanism. In addition, the accommodation response has been shown to be influenced by the changes in spherical aberrations.17,18 The exact mechanism of the internal optics compensation after decoupling of corneal and lenticular aberration following a refractive surgery procedure is still unclear and remains to be addressed.
Another reason might be that in our former study, we analyzed the postoperative whole eye aberrations through a 5-mm pupil, whereas we used a 6-mm pupil in this study. When calculating the induced spherical aberrations through a 5-mm pupil in the present study, we would obtain an induction of 0.10 μm RMS spherical aberration instead of 0.27 μm, which represents a decrease of more than 60%. Therefore, the difference in pupil size and the relative preservation of the balance between corneal and ocular aberrations after refractive surgery as suggested by Gatinel et al7 seems to be a reasonable explanation for the discrepancy in results between our present and former studies on aspheric profiles.
The drawback of this study is that we did not measure the whole eye aberration to compare it to the induction of corneal HOA after aspheric ablation. However, the measurement of both corneal and ocular aberrations with two different instruments might introduce errors due to the two different measurement axes of the corneal topographer and the commercially available aberrometers. In addition, the relevance of comparing corneal and ocular aberrations after using two different instruments has already been questioned.7,19
Although no significant induction of corneal spherical aberration or change in eccentricity after low myopic ablation with the wavefront-optimized profile occurred, it remained significant after moderate and high myopic treatment. The magnitude of induced corneal HOA after aspheric ablation was related to the level of corrected ametropia. Further analysis with the same methodology and same instrument would be interesting in comparison of other ablation profiles and correlation of postoperative total ocular wavefront.