Subjects

Data were obtained from five eyes of five normal, male domestic short hair cats (*Felis cattus*), who underwent myopic PRK with an uncomplicated follow-up of at least 3 months and in which wavefront aberrations could be measured over a PD of 9 mm. Procedures were conducted according to the guidelines of the University of Rochester Committee on Animal Research (UCAR), the ARVO Statement for the Use of Animals in Ophthalmic and Vision Research, and the NIH Guide for the Care and Use of Laboratory Animals.

Photorefractive Keratectomy

Three cats’ eyes underwent PRK for −6 D, two with a programmed OZ of 6 mm and one with an 8-mm OZ; two eyes received a PRK for −10 D (6 mm OZ). The procedure has been described in detail elsewhere.^{23} Briefly, all eyes received a conventional spherical ablation (Planoscan 4.14; Bausch & Lomb, Inc., Rochester, NY) performed by one of two surgeons (SM, JB) in animals under surgical anesthesia (Technolas 217 laser; Bausch & Lomb, Inc.). The ablation was centered on the pupil, which was constricted with 2 drops of pilocarpine 3% (Bausch & Lomb). After surgery, the cats received 2 drops of 0.3% tobramy-cin+0.1% dexamethasone 0.1% (Tobradex; Alcon, Fort Worth, TX) per eye, once a day, until the surface epithelium healed.

Wavefront Sensing

As described previously,^{23}^{,}^{24} the cats were trained to fixate single spots of light presented on a computer monitor. Wavefront measurements were performed before surgery and 19±7 (12–24) weeks after surgery, with a custom-built Hartmann-Shack wavefront sensor. The wavefront sensor was aligned to the visual axis of one eye, while the other eye fixated a spot on the computer monitor.^{24} At least 10 spot-array patterns were collected per imaging session per eye.

Calculation of Centered WFE Differences

From each single spot–array pattern, WFEs were calculated with a 2nd–10th-order Zernike polynomial expansion according to Vision Science and Its Application (VSIA) standards for reporting aberration data of the eye.^{25} WFE changes were simulated in a multistep process. The *first step* included the determination of the center of the OZ. Because PRK was performed with the cat under general anesthesia and the ablation was registered to the pupil center, an alignment to the visual axis of the cat’s eye during surgery could not be ensured, and possible decentration effects had to be compensated for. Therefore, the centroiding area (analysis pupil) of 6-mm diameter was shifted manually in steps of 300 *μ*m according to the distance between the lenslet centers to find the wavefront that yielded the most negative *Z*_{2}^{0} value (i.e., the maximum treatment effect. This was defined as the centered, postoperative wavefront (W_{post}[*x*, *y*]), which was then averaged from single measurements over a PD of 9 mm. In the *second step*, the horizontal and vertical offsets between the center of the OZ and the center of the original pupil were used to calculate preoperative WFEs (W_{pre}[*x*,*y*]), for the position that equaled the later treatment center. Like W_{post}(*x*, *y*), W_{pre}(*x*, *y*) was computed for a 9-mm PD. In a *third step*, the change in WFEs, ΔW(*x*, *y*), were obtained by subtracting the pre- from the postoperative Zernike coefficients. Thus, ΔW(*x*, *y*) reflected the treatment effect over a 9-mm PD, for a perfectly centered OZ, minimizing the potential influence of internal aberrations. The Zernike coefficient spectrum of each ΔW(*x*, *y*) () was consistent with data obtained in humans after PRK.^{22}

| **Table 1**Treatment Characteristics and WFE Changes for the Centered Treatment (ΔW[*x*, *y*]) over 6- and 9-mm PDs |

Computer Modeling of Treatment Decentration

For each eye, decentration of a 6-mm subpupil relative to ΔW(*x*, *y*) was simulated by using custom software (MatLab 7.2; The MathWorks Inc., Natick, MA). Decentered WFE differences ΔW(*x*′, *y*′) were calculated for the size of the 6-mm subaperture along Cartesian decentrations Δ*x* and Δ*y*, where Δ*x* and Δ*y* were changed in steps of 100 *μ*m, covering the entire 9-mm centroiding area and resulting in a maximum decentration range of 3000 *μ*m over a circular region. Zernike polynomials for the 2nd to the 6th order were fitted to the data of each decentered wavefront ΔW(*x*′, *y*′) by using a singular value decomposition algorithm to calculate the pseudoinverse of the Zernike data to get the decentered subpupil Zernike coefficients. As a refinement of the manual determination of the centered position, the algorithm assigned the centered coordinates (Δ*x* = 0, Δ*y* = 0) to the ΔW(*x*′, *y*′) with the lowest Z_{2}^{0} value. For each eye, 709 WFEs, 1 centered and 708 decentered were calculated over a 6-mm PD.

Simulation of Decentered Treatment Effects and VSOTF Calculation

Theoretical optical quality was investigated by calculating the VSOTF metric (visual Strehl ratio based on the optical transfer function [OTF]). The VSOTF is the ratio of the contrast sensitivity–weighted OTF to the contrast sensitivity–weighted OTF of the diffraction-limited eye.^{26}^{,}^{27} Because the preoperative WFEs W_{pre}(*x*, *y*) were decentered, calculating the VSOTF from preoperative HOA could lead to misinterpretation of optical quality due to over- or underestimation of HOA. Thus, we calculated a standard preoperative WFE, W_{meanpre}(*x*_{0}, *y*_{0}), from all eyes included in this study. For the calculation of W_{meanpre}(*x*_{0}, *y*_{0}), all preoperative, pupil-centered WFEs were averaged, resulting in a WFE representing the typical preoperative range of HOA ().^{24}^{,}^{28} Simulated postoperative WFEs, W_{post}(*x*′, *y*′), were calculated by subtracting the W_{meanpre}(*x*_{0}, *y*_{0}) from each ΔW(*x*′, *y*′). This treatment simulation relative to a standard preoperative WFE allowed us to eliminate interindividual differences in preoperative optical quality and internal optics. Therefore, the independent variables in this experiment were the five different centered treatment effects ΔW(*x*, *y*) and their corresponding ΔW(*x*′, *y*′). A computer program (Visual Optics Laboratory, VOL-Pro 7.14; Sarver and Associates, Carbondale, IL) was used to calculate the VSOTF over an analysis PD of 3.5 and 6.0 mm. The VSOTF for a given WFE was calculated for the combination of LOA terms that provided the highest VSOTF simulating the optical quality with best spherocylindrical correction (BCVSOTF). Thus, for each simulated W_{post}(*x*′, *y*′), an LOA-derived refractive error based on 2nd-order terms and an “effective” refractive error based on the BCVSOTF were obtained. Differences between refractive errors were expressed as dioptric power vectors (*M*, *J0*, *J45*), where *M* corresponds to the spherical equivalent and *J0* to the 0°/90° and *J45* to the 45°/135° astigmatic components. The difference between the VSOTF- and 2nd-order–based power vectors could be considered a function of the interaction between HOA and LOA. Since “sphere” and “cylinder” are most commonly used in clinical settings, we displayed most of the results in terms of sphere and cylinder magnitude. To visualize decentration effects for single eyes, color maps plotting ΔLOA, ΔHOA, and Δlog BCVSOTF against horizontal and vertical decentration were created. For further statistical analysis, data for decentration along the 0°, 90°, 180°, and 270° meridians were averaged for each eye.

| **Table 2**The Averaged Preoperative Mean WFE W_{meanpre}(*x*_{0}, *y*_{0}), Computed for 3.5- and 6-mm PDs |

Calculating Decentration Tolerance

Analysis of tolerance was performed by calculating the maximum permissible decentration that yielded a critical refraction or BCVSOTF difference. For sphere and cylinder, this threshold value was defined a priori as −0.5 D. For the optical quality metric BCVSOTF, we chose a critical decrease of 0.2 log units, which roughly equals a decrease of 2 logMAR steps.

^{27} For each parameter investigated, vectors

*r* between the centered position (

*x*,

*y*) and each outmost coordinate below the criterion (threshold coordinates

*x*′,

*y*′) were calculated. The mean value,

, reflects the average maximum permissible decentration (in micrometers) that allows one to remain below the threshold criterion and equals the radius of a circle around the centered position. The standard deviation (

*SD*) of

and the coefficient of variation (

*CV*) of

served as metrics for regularity of decentration effects, where

*SD* of

reflects the absolute and

*CV* of

the relative irregularity. The smaller the

*SD* and

*CV*, the less variable were the decentration effects along different meridians (i.e., the more circle-shaped was the decentration pattern).

Statistical Analysis

All analyses were based on the difference values Δ*W* and Δ log BCV-SOTF, which reflected the treatment effects. Main outcome measures were the change of log BCVSOTF, the change of LOA, expressed in diopters, and the change of HOA as a function of decentration. All differences for the center position (*x*, *y*) were normalized to zero. Thus, values for decentered coordinates *x*′ and *y*′ reflect the deviation from the centered treatment effect. The difference between wavefront-and VSOTF-based refraction was considered an effect of interaction between LOA and HOA. Tolerance metrics were calculated as described earlier. HOAs were broken down into coma root mean square (RMS) (the RMS of all coma terms Z_{n}^{±1}), spherical aberration RMS (SA RMS, the RMS value of all coefficients Z_{n}^{0}), and the RMS of the residual noncoma, nonspherical aberrations (rHOA, the RMS value of all remaining HOA Z_{n}^{≥2}).

The influence of the magnitude of HOA induction on decentration tolerance was assessed with linear regression analysis. The dependent variables were the mean vectors

and their

*SD*. To investigate the impact of HOAs on log BCVSOTF, we applied a multiple-regression model using HOAs as predictors and log BCVSOTF as dependent variables. The role of interaction on decentration tolerance was investigated by comparing

and

*SD* for 2nd-order sphere and cylinder with their VSOTF-based equivalents using a nonparametric test for matched pairs (Wilcoxon test). The same test was also applied to compare decentration tolerance for PDs of 3.5 and 6.0 mm. All statistical tests were performed with a commercial program (SPSS 11.0; SPSS Inc., Chicago, IL), assuming a significance level of

*P* < 0.05 and using the Bonferroni adjustment for multiple tests.