#### Abstract

To investigate whether the Estimated Pre-Refractive SimK accurately predicts the preoperative corneal power (K) in eyes with previous myopic femtosecond laser-assisted LASIK (FS-LASIK) and whether a better prediction can be developed.

Preoperatively and 3 months after FS-LASIK, patients underwent anterior segment imaging with the Pentacam HR rotating Scheimpflug camera (Oculus Optikgeräte, Wetzlar, Germany). Posterior and anterior corneal curvature and power and asphericity (Q-value at 8 mm) were recorded. Multiple linear regression was used to assess the relationship among variables.

One hundred four eyes of 104 patients were enrolled. The Estimated Pre-Refractive SimK (43.19 ± 1.63 diopters [D]) was lower (*P* = .0014) than the mean preoperative K (43.44 ± 1.49 D). The difference was within ±0.50 and ±1.00 D in 53.8% and 86.5% of eyes, respectively. Multiple linear regression detected a statistically significant relationship (*r*^{2} = 0.8497, *P* < .0001) among the investigated parameters: preoperative anterior corneal radius = 1.156 + 1.012 * postoperative posterior corneal radius – 0.3800 * postoperative Q-value. When this equation was used to predict the preoperative K, the difference between the actual preoperative K and the predicted value (43.41 ± 1.38 D) was not statistically significant. The rate of eyes with a difference between the predicted and actual preoperative K within ±0.50 and ±1.00 D increased to 61.5% and 93.3%, respectively.

The corneal power before FS-LASIK can be accurately predicted from the postoperative corneal measurements of a rotating Scheimpflug camera. The multiple regression formula described may be more accurate than the Estimated Pre-Refractive SimK available on the Pentacam.

**[ J Refract Surg. 2016;32(5):332–336.]**

The reduced accuracy of intraocular lens (IOL) power calculation in eyes with previous laser refractive corneal surgery depends on three main errors: the instrument error, the index of refraction error, and the formula error.^{1} This study aimed to minimize the formula error.

The formula error is due to the incorrect estimation of the effective lens position (ELP) by the Hoffer Q, Holladay 1, and SRK/T formulas,^{2–4} which use the corneal power (K) derived from the anterior corneal curvature to predict the ELP. Because the K is artificially changed by photorefractive keratectomy (PRK) and LASIK, the above-mentioned formulas will predict an erroneous ELP if the postoperative K is entered. For example, if the postoperative K after myopic correction is entered into these formulas, the predicted ELP will be too low, the IOL power will be underestimated, and the final refraction will be more hyperopic. One solution to this error is the Double-K method by Aramberri,^{5} who suggests using the pre-PRK or pre-LASIK K to predict the ELP and the post-PRK or post-LASIK K (modified to avoid the instrument error and the index of refraction error) for the vergence formula. Unfortunately, the preoperative K is often unavailable. In this event, the simplest approach is to rely on the mean K value reported in the literature (eg, 43.81 diopters [D]).^{6} The Pentacam HR (Oculus Optikgeräte, Wetzlar, Germany), a rotating Scheimpflug camera, offers a technological alternative because it provides surgeons with an “Estimated Pre-Refractive SimK,” which has received little to no attention in the literature.

The purpose of this study was two-fold. First, we aimed to assess how close this value estimated by the Pentacam is to the original K in a sample of eyes that underwent femtosecond laser-assisted LASIK (FS-LASIK) to correct either myopia or myopic astigmatism. Second, we aimed to investigate whether a new regression formula may allow us to better predict the pre-LASIK K.

### Patients and Methods

This prospective study included all consecutive patients operated on between September 2012 and July 2014 using FS-LASIK for myopia or myopic astigmatism. Each patient was informed of the purpose of the study and gave written consent to participate. The study protocol was approved by the local ethics committee of Fondazione G.B. Bietti IRCCS and the methods adhered to the tenets of the Declaration of Helsinki for research involving human subjects.

Each patient underwent bilateral FS-LASIK performed using the FS200 femtosecond laser (WaveLight Laser Technologie AG, Erlangen, Germany) and the EX500 excimer laser (WaveLight Laser Technologie AG). The flap thickness was set at 120 microns and the planned flap diameter was 9 mm in all cases. After surgery, patients were prescribed 0.3% netilmycin and 0.1% dexamethasone (Netildex; SIFI, Catania, Italy) to be taken four times a day for the first week and preservative-free artificial tears to be taken every hour for the first day and then tapered off over the following 3 months.

Preoperatively, all eyes underwent subjective manifest and cycloplegic refractions, slit-lamp examination of the anterior segment, intraocular pressure measurement, indirect ophthalmoscopy, and anterior segment imaging with the Pentacam HR rotating Scheimpflug camera (software version 1.20r10). Scans were taken in the automatic release mode. Of the different scanning options available, the 25-picture scan was used. Only scans that had an examination quality specification graded by the instrument as “OK” were saved. The postoperative evaluation was performed after 3 months and included manifest and cycloplegic refraction and anterior segment Scheimpflug imaging.

The pre-LASIK K was registered. Among the several values provided by the rotating Scheimpflug, the average of K1 and K2 was considered because these values correspond to simulated keratometry and should therefore be entered into IOL power calculation formulas. The K1 and K2 values are calculated using the 1.3375 keratometric index and the measured radius of the anterior corneal surface, by means of the formula: Corneal power = (1.3375 – 1) / anterior corneal radius.

Preoperatively, the mean anterior and posterior corneal radii, the ratio between them, and the posterior Q-value (at 8 mm) were recorded. The Q-value is an expression of the shape factor of the conic curve that best fits the aspheric surface of the cornea.^{7}

At 3 months after surgery, the Estimated Pre-Refractive SimK provided in the Holladay Report was registered and used for further analysis. This value is calculated based on a proprietary algorithm that has not been published ( http://www.hicsoap.com/docs/Pentacam-Holladay-Report-Interpretation-Guidelines-FINAL-DRAFT-JTH-19oct14-(1.6%20MB).pdf, accessed on October 14, 2015).

#### Statistical Analysis

All statistical tests were performed using GraphPad InStat (version 3a) for Macintosh (GraphPad Software, San Diego, CA). Because all patients had bilateral surgery, only one randomly chosen eye was considered for statistical analysis. Normal distribution was assessed by means of the Kolmogorov–Smirnov test. Paired data were compared using the *t* test (in the case of a normal distribution) or Wilcoxon matched-pairs test (in the case of a non-normal distribution). Linear regression and multiple linear regression were used to assess the relationship between variables. Agreement between the predicted and the actual preoperative K was evaluated using Bland–Altman analysis, in which the differences between these values are plotted against their mean. The 95% limits of agreements (LoAs) were defined as the mean ± 2 standard deviations (SD) of the differences between the actual and the predicted values.

### Results

One hundred four eyes of 104 patients (58% females; mean age: 35.3 ± 8.9 years; range: 20 to 75 years) were enrolled. The mean spherical equivalent correction was −4.09 ± 2.10 D and ranged from −1.25 to −9.00 D. The mean postoperative spherical equivalent was −0.05 ± 0.38 D (range: −0.50 to +0.50 D). The mean preoperative anterior and posterior corneal radii of curvature were 7.78 ± 0.27 and 6.41 ± 0.25 mm, respectively, and showed a good correlation (*r*^{2} = 0.8106, *P* < .0001) (**Figure 1**). The mean ratio between the preoperative anterior and posterior corneal radii of curvature (A/P ratio) was 1.21 ± 0.02 and ranged from 1.17 to 1.25. The mean posterior Q-value was −0.34 ± 0.14 and ranged from −0.69 to −0.05.

Figure 1. Linear regression showing the strong relationship between the anterior and posterior corneal radii before surgery. |

Regarding the postoperative measurements, the mean anterior corneal radius increased to 9.35 ± 0.45 mm (*P* < .0001). The mean posterior corneal radius was 6.43 ± 0.25 mm (ie, 0.02 mm steeper than the preoperative value); this difference was statistically significant (*P* < .0001), but not clinically relevant. No eyes showed any sign of corneal ectasia. The mean posterior Q-value was −0.31 ± 0.15 (range: −0.65 to 0.01); again, the difference compared to the preoperative value was statistically (*P* < .0001) but not clinically significant.

#### Comparison Between the Preoperative K and the Estimated Pre-Refractive SimK

We found a statistically significant difference between the mean preoperative K (43.44 ± 1.49 D) and the Estimated Pre-Refractive SimK from the Holladay report (43.19 ± 1.63 D) (*P* = .0014, Wilcoxon matched-pairs test for nonparametric data). The difference between the preoperative K and the estimated SimK ranged from −1.50 to +2.50 D. The Estimated Pre-Refractive SimK was within ±0.50 and ±1.00 D of the preoperative value in 53.8% and 86.5% of eyes, respectively (these rates would have been 59.6% and 67.3%, respectively, had the above-mentioned mean value of 43.81 D been used). Bland–Altman analysis revealed that the 95% LoAs ranged between −1.20 and 1.71 D.

Linear regression showed that the difference between the actual and the predicted preoperative K was correlated to the A/P ratio (*r*^{2} = 0.8291, *P* < .0001). In patients with a lower A/P ratio (ie, with a steeper anterior corneal curvature in comparison to the posterior corneal curvature), the preoperative K was higher than the estimated K (**Figure 2**).

Figure 2. Linear regression showing that the difference between the real and the estimated preoperative corneal power is correlated to the ratio between the anterior and posterior corneal radii. |

#### New Regression Formula to Estimate the Pre-Refractive K

Multiple linear regression detected a statistically significant relationship (*r*^{2} = 0.8497, *P* < .0001) among the preoperative anterior corneal radius, the postoperative posterior corneal radius, and the postoperative Q-value, according to :

The *r*^{2} coefficient was higher when both postoperative parameters were considered than when just the posterior corneal radius (*r*^{2} = 0.8062) or posterior Q-value (*r*^{2} = 0.0071) was separately considered.

To improve the prediction accuracy, we recalculated the preoperative radius and K using . After we did so, the difference between the actual preoperative K (43.44 ± 1.49 D) and the estimated preoperative value (43.41 ± 1.38 D) was no longer statistically significant (*P* = .45). The rate of eyes where the error in predicting the preoperative K was within ±0.50 and ±1.00 D of the preoperative value increased to 61.5% and 93.3%, respectively. The 95% LoAs improved to between −1.10 and 1.16 D. Again, linear regression analysis showed that the difference between the actual and the predicted preoperative K was correlated to the A/P ratio (*r*^{2} = 0.5598, *P* < .0001). All eyes (n = 3) with a preoperative K steeper than the estimated K value by more than 1.00 D had an A/P ratio less than 1.185. On the other hand, all eyes with a preoperative K flatter than the estimated K value by more than 1.00 D had an A/P ratio greater than 1.239.

### Discussion

Preoperative K is required to calculate the IOL power after refractive surgery when Double-K formulas are used.^{5} These are necessary with all methods aiming to overcome the index of refraction and instrument errors and relying on the Hoffer Q, Holladay 1, or SRK/T formulas. Examples of methods requiring the Double-K adjustment are those described by Awwad et al.,^{8} Wang et al.,^{9} Maloney,^{10} Savini et al.,^{11} and Seitz and Langenbucher,^{12} Speicher et al.,^{13} the clinical history method,^{14,15} and the total K measurements provided by most Scheimpflug cameras^{16–20} and optical coherence tomography.^{21} Because the preoperative K is required by so many methods and is often unknown, it is surprising that its estimation from postoperative data received so little attention in the literature.

The first objective of this study was to assess the accuracy of the Estimated Pre-Refractive SimK given in the Holladay Report of the Pentacam. Our data suggest that it provides a moderately good estimation of the preoperative K. The difference between them would have been within ±1.00 D in a higher percentage of eyes (86.5%) compared to the alternative of using the mean value of 43.81 D (67.3%) reported by Hoffer in 1980. However, the Estimated Pre-Refractive SimK was within ±0.50 D of the actual preoperative value in only half of patients and its mean value revealed a statistically significant difference in comparison to the mean preoperative K. This led us to our secondary objective, the search for a more accurate prediction. Our data showed that the regression formula we have described would enable us to increase the rate of eyes with an estimated K within ±0.50 and ±1.00 D of the preoperative value and eliminate the statistical difference with respect to the real preoperative K.

The Estimated Pre-Refractive SimK generated by the Holladay Report of the Pentacam has received little attention in the peer-reviewed literature. We could not find published articles describing the methods and formulas used to calculate this value, although it is logical to expect that it is based on the postoperative posterior corneal curvature. The only study that investigated it found results different from ours. Falavarjani et al. did not, in fact, detect any statistically significant difference between the Estimated Pre-Refractive SimK and the preoperative K in a sample of 35 eyes that had undergone myopic photorefractive keratometry.^{22} This discrepancy between our study and that of Falavarjani et al. may be due to their smaller sample size.

Other authors have looked for alternative methods to take advantage of Scheimpflug measurements when estimating the preoperative K. Saiki et al.^{23} described a regression formula based on the postoperative posterior K, but their results cannot be replicated because they used a 6-mm diameter posterior K measurement that is not commercially available. Moreover, they did not report the rate of eyes where the estimated K was within ±0.50 or ±1.00 D of the actual preoperative K. Hence, it is not possible to compare our findings to theirs.

By contrast, our formula can be easily computed and adopted by any clinician because the required parameters are displayed automatically by the Scheimpflug camera. It offers good accuracy in predicting the preoperative K because the estimated value was within ±1.00 D of the actual preoperative value in more than 90% of eyes. Further improvements may be evaluated with the aim of achieving even better agreement. A major obstacle to this goal is represented by the high variability of the A/P ratio, which ranged from 1.17 to 1.26 in our sample and had an even larger range (from 1.09 to 1.39) in a previous study.^{24} Our data show that when the preoperative A/P ratio is high (ie, when the preoperative anterior corneal radius is flatter than in the average case), the prediction formula tends to estimate a K value that is too high. The opposite occurs in eyes with a low preoperative A/P ratio. Therefore, the variability of the relationship between the anterior and posterior corneal curvature hampers a perfect estimation of the preoperative anterior corneal radius from the postoperative posterior corneal radius. There is currently no method to calculate this ratio once the anterior corneal surface has been modified by the excimer laser.

There are some limitations in our study. First, we investigated only eyes that underwent a myopic correction, so further analysis is needed for eyes with previous hyperopia. Second, we obtained postoperative measurements at 3 months. The statistical differences in the posterior corneal curvature that we observed were not clinically relevant and were not associated with any sign of corneal ectasia. Although previous studies have shown that FS-LASIK does not change the posterior corneal curvature,^{25–27} a longer follow-up may reveal slightly different results for the regression formula. Third, the regression formula described in our study should be validated in an external sample.

We found that the postoperative measurements obtained by the Scheimpflug instrument can help predict the preoperative K in the majority of eyes and generate a value that is more accurate than the generic mean preoperative value.

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