Intraocular lens power calculation after myopic excimer laser surgery: Clinical comparison of published methods

ARTICLE

Intraocular lens power calculation after myopic excimer laser surgery: Clinical comparison of published methods Giacomo Savini, MD, Kenneth J. Hoffer, MD, Michele Carbonelli, MD, Piero Barboni, MD

PURPOSE: To compare results of intraocular lens (IOL) power calculation methods after myopic excimer laser surgery. SETTING: Private practice. METHODS: In this prospective study, eyes having phacoemulsification after myopic excimer laser surgery were classified into Group 1 (preoperative corneal power available, refractive change known), Group 2 (preoperative corneal power available, refractive change uncertain), and Group 3 (preoperative corneal power unavailable, refractive change known even if uncertain). The IOL power was calculated using the following methods: clinical history, Awwad, Camellin/Calossi, Diehl, Feiz, Ferrara, Latkany, Masket, Rosa, Savini, Shammas, Seitz/Speicher, and Seitz/Speicher/Savini. RESULTS: The lowest mean absolute errors (MAEs) in IOL power prediction in Group 1 (n Z 12) and Group 2 (n Z 11), respectively, were with the methods of Seitz/Speicher/Savini (0.51 diopter [D] G 0.44 [SD] and 0.55 G 0.50 D), Seitz/Speicher (0.58 G 0.47 D and 0.54 G 0.45 D), Savini (0.60 G 0.44 D and 0.65 G 0.63 D), Masket (0.82 G 0.49 D and 0.69 G 0.51 D), and Shammas (0.77 G 0.43 D and 1.11 G 0.50 D). In Group 3 (n Z 5), the lowest MAEs were with the methods of Masket (0.23 G 0.27 D), Savini (0.49 G 0.86 D), Seitz/Speicher/Savini (0.68 G 0.36 D), Shammas (0.84 G 0.98 D), and Camellin/Calossi (0.91 G 0.84 D). CONCLUSIONS: When corneal power is known, the Seitz/Speicher method (with or without Savini adjustment) seems the best solution to obtain an accurate IOL power prediction. Otherwise, the Masket method may be the most reliable option. Financial Disclosure: No author has a financial or proprietary interest in any material or method mentioned. J Cataract Refract Surg 2010; 36:1455–1465 Q 2010 ASCRS and ESCRS

Over the past decade, an impressive number of methods and formulas have been devised with the aim of improving the accuracy of intraocular lens (IOL) power calculation in eyes that have had excimer laser myopic correction and that require cataract extraction with IOL implantation.1–29 In these cases, IOL power calculation can lead to unexpected refractive outcomes for 2 primary reasons. The first is that the surgically induced corneal power change is underestimated because the standard keratometric refractive index (usually 1.3375) is not valid once the laser modifies the anterior to posterior corneal curvature ratio.30–33 The second reason is that the IOL position is erroneously predicted by third-generation theoretical formulas (eg, Hoffer Q, Holladay 1, SRK/T)34–37 that derive the prediction from the corneal curvature.8 Q 2010 ASCRS and ESCRS Published by Elsevier Inc.

A third reason may be partially responsible for the inaccuracy of IOL power calculation for eyes with a small optical zone and large correction; in this case, the difference between the paracentral corneal area (where keratometry [K] and simulated K readings are taken) and the central cornea area (where the visual axis passes) can be clinically relevant.31,38–40 In 2006, our group evaluated the accuracy, from a theoretical viewpoint, of methods that were developed to solve the problem of inaccurate IOL power calculation.21 Since then, other formulas have been described, and surgeons can now choose from many methods. This can easily generate confusion rather than accuracy. The aim of the present study was to assess the clinical performance of older and newer methods of calculating IOL power in a relatively large 0886-3350/$dsee front matter doi:10.1016/j.jcrs.2010.02.029

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sample of patients who had phacoemulsification and IOL implantation after myopic photorefractive keratectomy (PRK) or laser in situ keratomileusis (LASIK).

were unknown. Because only 1 eye was classified into Group 4, this group was not included in the comparative analysis.

Intraocular Lens Power Calculation PATIENTS AND METHODS This prospective study included data of eyes of patients directly examined by 1 surgeon (G.S.) or submitted via e-mail by other surgeons who sought an opinion on which IOL power to implant in a specific eye. The analysis was performed between September 2005 and November 2009. All patients provided informed consent, and the study methods adhered to the tenets of the Declaration of Helsinki for the use of human participants in biomedical research. Exclusion criteria included vitreoretinal or corneal disease; a history of other ocular surgery, uveitis, trauma, or systemic disease affecting vision; and intraoperative complications (during refractive or cataract surgery). The following data were requested from the surgeons who sent an e-mail requesting an IOL power: A-constant of the IOL to be implanted, axial length (AL) measured by immersion ultrasound biometry or partial coherence interferometry (PCI) (IOLMaster, Carl Zeiss Meditec), current corneal power (measured by corneal topography or IOLMaster) and, if available, preoperative corneal power, preoperative refraction, and postoperative refraction (before cataract onset). Moreover, a copy of the last corneal map was requested to exclude eyes with a decentered laser treatment, which can cause irregular corneal curvatures. For preoperative and postoperative corneal power measurements obtained by corneal topography, the simulated K value was considered and used for further calculations. Because data were provided by 12 surgeons, several corneal topographers were included such as the TMS-2 (Tomey Corp.), Keratron (Optikon 2000), CM02 (Costruzione Strumenti Oftalmici), and EyeSys System 3000 (EyeSys Vision). To assess the accuracy of the IOL power calculation methods in different clinical scenarios, 4 possible conditions were defined and the patients classified accordingly. In Group 1, the preoperative corneal power was available and the preoperative and postoperative refractions (ie, the surgically induced refractive change) were known and certain. In Group 2, the preoperative corneal power was available and the surgically induced refractive change was known but uncertain, in most cases because the postoperative refraction was unknown. In Group 3, the preoperative corneal power was unknown but the surgically induced refractive change was known, even if uncertain. In Group 4, the preoperative corneal power and surgically induced refractive change

Submitted: December 23, 2009. Final revision submitted: February 19, 2010. Accepted: February 23, 2010. From the G.B. Bietti Eye Foundation–IRCCS (Savini), Rome, and Studio Oculistico d’Azeglio (Carbonelli, Barboni), Bologna, Italy; Jules Stein Eye Institute (Hoffer), University of California, Los Angeles, California, USA. Corresponding author: Giacomo Savini, MD, G.B. Bietti Eye Foundation–IRCCS, Via Livenza 3, Rome, Italy. E-mail: giacomo.savini@ alice.it.

For each eye, IOL power was calculated with 2 categories of methods. The first category included methods that adjust the overestimation of corneal power.1–4,6,9,10,17,21,24, 25 The second category included methods that have been developed to directly correct the calculated IOL power (and not the corneal power).5,12,14,18,19,26 Table 1 shows the methods. The corneal powers obtained with the first category of methods and the simulated K were entered into the double-K SRK/T formula to obtain the IOL power.8 The only exceptions were the Shammas no-history method (values entered into the Shammas PL formula, as recommended by authors),41 the methods of Rosa and Ferrara (values entered into the single-K SRK/T formula based on results in previous study21), the Awwad method (values entered into double-K Holladay 1 formula because method derived Table 1. Methods included in the study. Method

Comment

Adjusts overestimation of corneal power Calculated at corneal Clinical history1,2 plane Seitz/Speicher: separate Advocated by Seitz consideration of anterior et al.3 in 2000 and later reviewed and posterior corneal by Speicher4 curvatures Savini modification of Proposed by Savini Seitz/Speicher et al.21 in the absence of preoperative corneal power data Both no-history and Shammas9 refraction-derived methods d Camellin/Calossi17 d Savini et al.24 Equation 2 Awwad25 d Rosa6 d Ferrara10 Directly corrects calculated IOL power Feiz Both methods described by Feiz et al.5 (ie, formula and nomogram) d Latkany14 Cornea bypass Described by Walter et al.18 and Ladas and Stark12 Masket19 d d Diehl26 IOL Z intraocular lens

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from Holladay 1 formula), and the clinical history method (values entered into double-K Hoffer Q formula as well as into double-K Holladay 1 and double-K SRK/T formula to ensure greater consistency with previous studies). The SRK/T formula was also used for the second category of methods. The choice of this formula was based on its demonstrated accuracy in long eyes.42 For eyes in Group 3, the preoperative corneal power to be entered into the double-K SRK/T was calculated by adding the refractive change (at the corneal plane) to the postoperative corneal power calculated according to the method of Speicher4 and Seitz and Langenbucher3 as modified by Savini et al.21 This approach was chosen because it provided lower mean absolute errors (MAEs) than when a default preoperative value close to the mean value of the population (ie, 43.5 diopters [D]) is used. Because few eyes had been examined with instruments such as the Pentacam Scheimpflug system (Oculus, Inc.), the Orbscan scanning-slit topographer (Bausch & Lomb), or the IOLMaster biometer or with specific corneal topographers such as the TMS topography system, Atlas (Carl Zeiss Meditec), or EyeSys system, the analysis in this study did not include methods relying on measurements and calculations obtained with these devices.11,22,23,25,27,29 Finally, the MAE and mean arithmetic error (ME) in IOL power prediction were calculated for each method. The IOL power prediction error was computed as the difference between the predicted IOL power and the back-calculated IOL power for emmetropia, with positive values indicating an overpredicted IOL power and a subsequent myopic refractive outcome. As in the method described by Aramberri8 and later adopted by other authors,28,43 the power of the back-calculated IOL for emmetropia (IOLem) was calculated for each case as follows: 1. Using the double-K SRK/T formula, the magnitude of IOL power that should produce 1.00 D of refractive change at the spectacle plane (IOL1DRx) was obtained by calculating the IOL power for a desired postoperative refraction of 1.00 D and for emmetropia and subtracting the latter from the former value. (In the study sample, the mean difference was 1.42 G 0.08 D; range 1.30 to 1.61 D.) 2. The IOL1DRx was then multiplied by the refraction error (Rx) and added to the implanted IOL power (IOLimp) so that the resulting formula was

IOLem Z IOL1DRx  Rx þ IOLimp The mean IOLem calculated using this method (17.36 G 2.61 D) was not statistically different from the mean value calculated using the method advocated by Feiz et al.5 (17.36 G 2.59 D;

P Z .72, paired t test), who related a change of 1.00 D in IOL power to a change of 0.70 D in refraction at the spectacle plane.

Statistical Analysis Only the first operated eye of patients having bilateral cataract surgery was included in the analysis unless the 2 eyes were classified into 2 different groups. All statistical tests were performed using GraphPad InStat for Macintosh software (version 3a, GraphPad Software). A paired t test was performed to analyze differences between groups and linear regression to analyze relationships between variants. Unless otherwise indicated, all data are expressed as the mean G SD. A P value less than 0.05 was considered statistically significant.

RESULTS Thirty-two eyes of 28 patients were prospectively analyzed. Six eyes of 4 patients were directly examined by the surgeon. The data for the other 26 eyes of 24 patients were submitted by e-mail by other surgeons. The mean age of the patients was 52.5 G 9.6 years. Sixteen eyes had PRK and 16 had LASIK. The mean interval between refractive surgery and cataract surgery was 8.4 G 3.1 years. Of the 32 eyes in the study, 12 were classified into Group 1, 12 into Group 2, 7 into Group 3, and 1 into Group 4. After 3 eyes of patients who had bilateral surgery and the 1 eye in Group 4 were excluded, the final sample comprised 28 eyes of 27 patients (PRK Z 15, LASIK Z 13). Table 2 shows the clinical features by group. Cataract extraction was performed by phacoemulsification in all cases; all surgeries were uneventful. The A-constant of the implanted IOL was 118.4 in 23 eyes, 119.0 in 2 eyes, 119.6 in 1 eye, 118.7 in 1 eye, and 118.5 in 1 eye. The target refraction was plano in 24 eyes, 1.00 D in 3 eyes, and 3.00 D in 1 eye. Overall, the mean difference between the target refraction and the spherical equivalent measured 1 month after cataract surgery was 0.43 G 0.59 D (range 1.50 and C0.25 D); the mean absolute difference was 0.49 G 0.47 D. Seventeen eyes (60.7%) were within G0.50 D

Table 2. Clinical features by group. Mean G SD Group 1 2 3

Sample (n)

AL (mm)

Preoperative K (D)

Surgically Induced Refractive Change (D)

12 11 5

27.71 G 1.97 27.78 G 1.26 28.03 G 2.46

43.76 G 1.09 43.17 G 1.63 Not available

7.75 G 3.65 8.19 G 3.45 9.57 G 4.19

AL Z axial length; K Z corneal power; NA Z not available

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Table 3. Mean corneal power calculated by the different methods. Method and Mean Corneal Power (D) G SD Group

Speicher/Seitz/ Savini

Speicher/Seitz

Savini

Shammas No History

Camellin/ Calossi

37.82 G 3.01 36.50 G 2.99 36.77 G 3.46

37.82 G 2.96 36.57 G 2.90 NA

37.72 G 2.98 36.45 G 2.90 36.58 G 3.36

37.00 G 3.08 35.66 G 3.06 35.94 G 3.54

36.91 G 2.97 35.65 G 2.89 35.76 G 3.34

1 2 3

NA Z not available *Corneal power measured by PCI optical biometry instead of corneal topography (simulated K) in 1 eye

of the intended refraction, 24 (85.7%) were within G1.00 D, and all were within G1.50 D. Table 3 shows the mean postoperative corneal power in each group calculated using the different methods. The simulated K value provided the highest mean corneal power in all groups, and the Ferrara variable refractive index method always resulted in the lowest power. When the preoperative corneal power was available and the refractive change induced by the laser was considered certain (Group 1), the lowest MAE in IOL power prediction was obtained with the Seitz/Speicher method, with or without the modification proposed by Savini et al. The method of Savini had a similar MAE, and good results were obtained with those described by Shammas, Masket, and Latkany. All other methods produced MAEs higher than 1.00 D (Table 4).

In Group 2, for which the refractive change was uncertain, the Seitz/Speicher method again produced the lowest MAE in IOL power prediction with or without the modification by Savini et al. The Savini method again gave the third lowest MAE followed by the Masket method. The Shammas no-history method was sixth, surprisingly preceded by the standard simulated K (entered into double-K SRK/T), which produced an MAE of 0.86 G 0.38 D (coupled, however, with a mean underestimation in IOL power of 0.79 G 0.51 D). The MAE for all other methods was higher than 1.00 D (Table 5). Given that the results in Groups 1 and 2 were similar, with the same methods providing the best results, the eyes in both groups were pooled to assess which method gives the lowest MAE, independent of the degree of certainty about the refractive change. Table 6

Table 4. Mean absolute and arithmetic errors in IOL power prediction for eyes in Group 1. Error in Power Prediction (D) Absolute

Arithmetic

Method

Mean G SD

Range

Mean G SD

Range

Seitz/Speicher/Savini Seitz/Speicher Savini Shammas no history Masket Latkany Diehl Simulated K Clinical history Camellin/Calossi Awwad Shammas refraction derived Feiz (formula) Feiz (nomogram) Rosa Walther (corneal bypass) Ferrara

0.51 G 0.44 0.58 G 0.47 0.60 G 0.44 0.77 G 0.43 0.82 G 0.49 0.86 G 0.63 1.08 G 0.76 1.13 G 0.69 1.29 G 1.28 1.32 G 0.69 1.42 G 0.87 1.46 G 0.89 1.47 G 1.11 1.83 G 1.26 1.89 G 1.19 2.19 G 1.81 3.75 G 1.71

0.00 to 1.19 0.08 to 1.41 0.14 to 1.46 0.15 to 1.58 0.04 to 1.59 0.25 to 2.39 0.23 to 3.03 0.07 to 2.37 0.31 to 4.53 0.30 to 2.71 0.16 to 2.58 0.35 to 2.97 0.05 to 3.60 0.37 to 4.35 0.49 to 4.29 0.31 to 5.36 0.65 to 6.05

0.07 G 0.68 0.06 G 0.76 0.08 G 0.75 0.31 G 0.85 0.39 G 0.90 0.63 G 0.88 0.55 G 1.24 0.95 G 0.93 0.76 G 1.68 1.26 G 0.80 1.39 G 0.91 1.46 G 0.89 0.83 G 1.69 1.83 G 1.26 1.89 G 1.19 1.83 G 2.20 3.75 G 1.71

1.19 to 1.15 1.41 to 1.13 1.42 to 1.46 0.87 to 1.58 1.59 to 0.95 0.70 to 2.39 1.33 to 3.03 2.37 to 0.59 1.14 to 4.53 0.34 to 2.71 0.16 to 2.58 0.35 to 2.97 1.57 to 3.60 0.37 to 4.35 0.49 to 4.29 1.46 to 5.36 0.65 to 6.05

K Z keratometry

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Table 3. (Continued) Method and Mean Corneal Power (D) G SD Simulated K

Awwad

Shammas Refraction-Derived

Clinical History

Rosa

Ferrara

38.42 G 2.70 37.24 G 2.69 37.49 G 3.11*

36.82 G 3.39 35.42 G 3.30 35.42 G 3.85

36.78 G 3.35 35.47 G 3.11 35.50 G 3.47

37.25 G 3.15 35.72 G 2.87 NA

34.43 G 4.23 33.00 G 3.35 33.36 G 3.77

32.55 G 4.79 31.53 G 3.69 31.25 G 5.38

shows the results. The method described by Seitz and Speicher (with or without the modification by Savini) outperformed the other methods. The Savini, Masket, and Shammas no-history methods all gave low MAEs, although the mean IOL power predicted by the Masket method was slightly underestimated (ie, on the hyperopic side). The clinical history method did not provide accurate IOL power calculations, whereas the simulated K provided a relatively low MAE, although the ME showed an IOL power underestimation. Several other methods in addition to the clinical history method unexpectedly resulted in a poor outcome, especially in eyes with higher myopic correction. This was the case with the Awwad, Diehl, and cornea bypass methods and the Feiz formula. The Awwad method provided a high MAE. Linear regression showed that the prediction error was correlated with the amount of preoperative myopia

(r Z 0.58, r2 Z 0.33, P Z .0036). However, because this method was originally developed on the basis of the double-K Holladay 1 formula, calculations in the present study were also performed using the latter formula. The result was a substantial improvement; the MAE dropped to 1.03 G 0.82 D and the ME dropped to 0.74 G 1.10 D. (Table 5 shows that a similar result with the double-K Holladay 1 formula was obtained with the Camellin/Calossi method.) By omitting cases with a preoperative refraction less than 8.00 D, the improvement would have been even more evident and the MAE would have decreased to 0.78 G 0.50 D. High MAEs were obtained using other methods; the results with these methods were significantly related to the amount of refractive change. This was the case with the Diehl method (r Z 0.62, r2 Z 0.38, P!.0015), Feiz nomogram (r Z 0.73, r2 Z 0.54,

Table 5. Mean absolute and arithmetic errors in IOL power prediction for eyes in Group 2. Error in Power Prediction (D) Absolute

Arithmetic

Method

Mean G SD

Range

Mean G SD

Range

Seitz/Speicher/Savini Seitz/Speicher Savini Shammas no history Masket Latkany Diehl Simulated K Clinical history Camellin/Calossi Awwad Shammas refraction derived Feiz (formula) Feiz (nomogram) Rosa Walther (corneal bypass) Ferrara

0.55 G 0.50 0.54 G 0.45 0.65 G 0.63 1.11 G 0.50 0.69 G 0.51 1.32 G 1.02 1.61 G 1.23 0.86 G 0.38 1.97 G 1.17 1.50 G 0.86 2.20 G 1.28 1.74 G 1.09 2.30 G 1.68 2.27 G 1.72 2.00 G 0.83 2.18 G 1.22 3.52 G 1.17

0.05 to 1.51 0.06 to 1.70 0.05 to 2.10 0.32 to 2.13 0.03 to 1.78 0.08 to 3.27 0.09 to 3.65 0.32 to 1.35 0.07 to 3.57 0.07 to 3.34 0.57 to 4.21 0.36 to 3.82 0.39 to 5.30 0.44 to 5.50 0.39 to 3.56 0.37 to 3.90 1.08 to 6.04

0.26 G 0.71 0.18 G 0.70 0.35 G 0.85 0.70 G 1.03 0.14 G 0.87 0.99 G 1.37 1.13 G 1.72 0.79 G 0.51 1.42 G 1.85 1.49 G 0.88 2.10 G 1.46 1.74 G 1.09 1.96 G 2.10 2.19 G 1.83 2.00 G 0.83 1.83 G 1.74 3.52 G 1.17

0.97 to 1.51 0.53 to 1.70 1.02 to 2.10 1.27 to 2.13 1.78 to 1.09 1.08 to 3.27 1.82 to 3.65 1.35 to 0.36 2.96 to 3.57 0.07 to 3.34 0.57 to 4.21 0.36 to 3.82 0.75 to 5.30 0.44 to 5.50 0.39 to 3.56 1.08 to 3.90 1.08 to 6.04

K Z keratometry

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Table 6. Mean absolute and arithmetic errors in IOL power prediction for eyes in Groups 1 and 2. Error in Power Prediction (D) Absolute

Arithmetic

Method

Mean G SD

Range

Mean G SD

Range

Seitz/Speicher/Savini Seitz/Speicher Savini Masket Camellin/Calossi (double-K Holladay 1) Shammas no history Simulated K Awwad (double-K Holladay 1) Latkany Diehl Camellin/Calossi (double-K SRK/T) Shammas refraction derived Clinical history Awwad (double-K SRK/T) Rosa Feiz (formula) Feiz (nomogram) Walther (corneal bypass) Ferrara

0.53 G 0.46 0.56 G 0.45 0.62 G 0.52 0.76 G 0.49 0.91 G 0.65 0.93 G 0.48 1.00 G 0.57 1.03 G 0.82 1.08 G 0.86 1.33 G 1.03 1.41 G 0.76 1.60 G 0.98 1.62 G 1.25 1.79 G 1.13 1.94 G 1.01 1.87 G 1.44 2.04 G 1.48 2.18 G 1.52 3.64 G 1.45

0.00 to 1.51 0.06 to 1.70 0.05 to 2.10 0.03 to 1.78 0.17 to 2.27 0.15 to 2.13 0.07 to 2.37 0.10 to 3.56 0.08 to 3.27 0.09 to 3.65 0.07 to 3.34 0.35 to 3.82 0.07 to 4.53 0.16 to 4.21 0.39 to 4.29 0.05 to 5.30 0.37 to 5.50 0.31 to 5.36 0.65 to 6.05

0.09 G 0.70 0.05 G 0.73 0.21 G 0.79 0.27 G 0.88 0.53 G 1.00 0.50 G 0.94 0.88 G 0.75 0.74 G 1.10 0.80 G 1.13 0.83 G 1.48 1.37 G 0.83 1.60 G 0.98 1.08 G 1.75 1.73 G 1.23 1.90 G 1.10 1.37 G 1.94 2.00 G 1.53 1.83 G 1.95 3.64 G 1.45

1.19 to 1.51 1.41 to 1.70 1.42 to 2.10 1.78 to 1.09 1.37 to 2.69 1.27 to 2.13 2.37 to 0.59 1.21 to 3.56 1.08 to 3.27 1.82 to 3.65 0.34 to 3.34 0.35 to 3.82 2.96 to 4.53 0.57 to 4.21 0.55 to 4.29 1.57 to 5.30 0.44 to 5.50 1.46 to 5.36 0.65 to 6.05

K Z keratometry

P!.0001), Feiz formula (r Z 0.49, r2 Z 0.24, P Z .0155), and cornea bypass method (r Z 0.46, r2 Z 0.21, P Z .0294). For all these methods, omitting cases with a preoperative refraction less than 8.00 D would have reduced the MAE. In Group 3, the lowest MAE was by the Masket method followed by the Savini method, Speicher/ Seitz method modified by Savini, and Shammas nohistory method. Good results were also obtained with the Awwad and Camellin/Calossi methods when the calculated corneal power was entered into the double-K Holladay 1 formula instead of the double-K SRK/T (Table 7). DISCUSSION For the methods that can be calculated when only a corneal topographer is available (without the need for specific instruments, such as Scheimpflug cameras), we attempted to assess which are the most accurate in calculating IOL power after excimer laser surgery. The best performers in all study groups were the methods proposed by Seitz/Speicher, Savini, Masket, and Shammas (no history). Good results were also obtained with the Camellin/Calossi and Awwad methods when the double-K/Holladay 1 was used instead of the double-K/SRK/T. As a secondary outcome, we were interested in the refractive outcomes in our sample. Overall, the MAE

in refraction prediction in our series (0.49 G 0.47 D) can be considered good because it is close to results in previous studies of patients who had not had laser excimer surgery.44–46 Surprisingly, the method of separately considering the anterior corneal curvature and posterior corneal curvature, first described by Seitz and Langenbucher3 and later reviewed by Speicher,4 has never received much attention and is thus rarely found in published comparative studies. In a previous theoretical study,21 our group suggested its high accuracy; however, it had not been confirmed in a clinical setting. In the present study, both the ME and MAE were close to zero. Therefore, this method could be considered the most accurate, at least when coupled with the double-K SRK/T formula. If the preoperative corneal power is unknown, the Seitz/Speicher method can be modified according to Savini et al.,21 who suggest using a mean value of –4.98 D for posterior corneal curvature. The Seitz/Speicher/Savini method (K Z simulated K  1.114  4.98) is similar to other methods like the one proposed by Maloney (K Z central corneal power  1.114  4.9) and the modified version developed by Wang et al.11 (K Z central corneal power  1.114  6.1), equation 6 of Awwad et al.25 (K Z simulated K  1.114  6.062) and, to a lesser extent, the Shammas et al.9 no-history method (K Z simulated K  1.14  6.8). The present study found that it is highly accurate,

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Table 7. Mean absolute and arithmetic errors in IOL power prediction for eyes in Group 3. Error in Power Prediction (D) Absolute

Arithmetic

Method

Mean G SD

Range

Mean G SD

Range

Masket Savini Seitz/Speicher/Savini Shammas no history Camellin/Calossi (double-K Holladay 1) Simulated K Awwad (double-K Holladay 1) Latkany Camellin/Calossi (double-K SRK/T) Diehl Rosa Shammas refraction derived Awwad (double-K SRK/T) Feiz (nomogram) Ferrara

0.23 G 0.27 0.49 G 0.86 0.68 G 0.36 0.84 G 0.98 0.91 G 0.84 0.93 G 0.68 1.34 G 0.88 1.44 G 0.76 1.69 G 0.92 1.74 G 1.21 1.77 G 1.48 2.09 G 1.15 2.18 G 1.39 3.17 G 1.48 3.94 G 2.58

0.05 to 0.71 0.05 to 2.03 0.28 to 1.26 0.03 to 2.44 0.22 to 1.97 0.21 to 1.64 0.41 to 2.79 0.21 to 2.16 1.04 to 3.32 0.13 to 2.88 0.02 to 3.69 0.52 to 3.69 0.54 to 4.16 0.99 to 4.35 1.33 to 7.82

0.05 G 0.71 0.49 G 0.86 0.18 G 0.82 0.53 G 1.22 0.71 G 1.05 0.85 G 0.81 1.17 G 1.13 1.44 G 0.76 1.69 G 0.92 1.74 G 1.21 1.76 G 1.49 2.09 G 1.15 2.18 G 1.39 3.17 G 1.48 3.94 G 2.58

0.71 to 0.16 0.05 to 2.03 0.74 to 1.26 0.75 to 2.44 0.27 to 1.97 1.64 to 0.21 0.41 to 2.79 0.21 to 2.16 1.04 to 3.32 0.13 to 2.88 0.02 to 3.69 0.52 to 3.69 0.54 to 4.16 0.99 to 4.35 1.33 to 7.82

K Z keratometry

even when used in cases in which the preoperative corneal power is known, where the original Seitz/Speicher method can also be used. Our data confirm those reported by Ho et al.,47 who found that the Seitz/ Speicher method modified according to Savini et al.24 is highly accurate. They found low ME and MAE errors (C0.03 G 0.73 D and 0.60 G 0.36 D, respectively) that are close to our results. Obviously, this method (developed for eyes for which the preoperative corneal power is not known) must be used in

conjunction with double-K formulas, which require entry of the preoperative corneal power. There are 3 possibilities to solve this contradiction: (1) calculate the preoperative corneal power by adding the refractive change to the postoperative corneal power (as we did in this study), (2) use a mean value such as 43.13,48 or (3) estimate the effective lens position (ELP), as suggested by Ho et al.47 We believe that the good results obtained with the Seitz/Speicher method (with or without the Savini

Figure 1. Decision tree showing the most reliable methods depending on the availability of data on preoperative corneal power and refractive change (Hx Z history; K Z keratometry). J CATARACT REFRACT SURG - VOL 36, SEPTEMBER 2010

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modification) are related to its total independence of the surgically induced refractive change (a likely source of errors). Our study found that changing the keratometric refractive index according to the formula suggested by Savini et al.24 provides an accurate estimation of the corneal power that can be used in the double-K SRK/T formula to achieve good IOL power prediction. This method did not seem to be affected by the accuracy of refractive change measurements because it performed well in Groups 1 and 2. Our results confirm those recently reported by Geggel,28 who found that this method is one of the most accurate and included it in a new consensus group. The regression formula described by Masket and Masket19 produced low MAEs in IOL power prediction in all study groups and can therefore be considered quite accurate, although the original Masket method was based on only the IOLMaster K values while we used the simulated K values provided by corneal topography. The ME was always negative, meaning that the mean IOL power was underestimated and that a slight hyperopic outcome can be expected, at least when the SRK/T formula is used. Geggel.28 reported a similar finding. In Group 3 eyes, for which the preoperative corneal power was unknown, the Masket method had a great advantage in that it omits the double-K step required by the Savini and Seitz/Speicher/Savini methods. The latter methods can be significantly influenced by the choice of the preoperative corneal power to be entered into the double-K formulas. In contrast, the Masket method (like the Shammas no-history method) does not have this drawback and may thus represent the most accurate approach when information about preoperative corneal power is lacking. The Shammas no-history method, originally called the clinically derived method,9 gave fairly accurate results in all study groups. Our results were slightly worse than those reported by Shammas and Shammas,41 whose MAE in IOL power prediction was 0.55 G 0.31 D in a sample of eyes without known preoperative corneal power (similar to Group 3 in the present study, in which an MAE of 0.84 G 0.98 D was obtained). The main advantage of this method, which can be appreciated especially in eyes for which the preoperative corneal power is not known, is that the corrected corneal power is used in the Shammas post-LASIK (Shammas-PL) formula and in this formula the ELP does not vary with the corneal curvature, which has been altered by the LASIK procedure. Therefore, this was the only method in which the corrected corneal power was not entered into the double-K SRK/T formula.

The results obtained using the Latkany method were slightly poorer than expected. The mean arithmetic was always positive (ie, IOL power overestimation).The following 3 reasons may explain the discrepancies between our results and those reported by Latkany et al.14 and Khalil et al.49: (1) We adopted the formula based on average corneal power, (2) our readings were derived from corneal topography, and (3) we measured AL by immersion ultrasound biometry. In contrast, Latkany et al. (1) preferred the regression formula based on the flattest K, (2) derived the original regression formula from manual K (Javal), and (3) used applanation ultrasound biometry. When entered into the double-K SRK/T formula, the corneal power calculated with the Camellin/Calossi method resulted in a relatively high MAE in IOL power prediction. The mean arithmetic was always positive, with a subsequent myopic outcome. The suboptimal results are probably due to the fact that this method was developed to be used with the Camellin/Calossi formula for IOL power calculation,17 which is a modified Binkhorst II formula,50 and not with the double-K SRK/T formula. The Camellin/ Calossi formula calculates the ELP from the preoperative anterior chamber depth, which unfortunately was not available in the majority of our eyes and hence could not be applied in our study. Considerably better results would have been obtained by entering the calculated corneal power into the double-K Holladay 1 formula. The Diehl method is the most recently described and has not been evaluated since its original publication.26 The calculation in this case depends on the refractive change induced by surgery, and for this reason the method provided the best result in Group 1. Entering the corneal power generated by the clinical history method into the double-K SRK/T formula gave a high MAE in IOL power prediction, not only in Group 2, in which the refractive change was uncertain by definition and the clinical history method was expected to be inaccurate, but also in Group 1, in which the refractive change was retrieved from clinical charts and considered certain. In this group of eyes, the clinical history method should have theoretically been the most accurate; however, only 7 of 12 eyes had an MAE in IOL power prediction less than 1.00 D. Further analysis showed that little change would be achieved by entering the corneal power into the double-K Hoffer Q or Holladay 1 formulas. The number of eyes with an MAE less than 1.00 D would increase with the double-K Hoffer Q (8 of 12) and would decrease with the double-K Holladay 1 (4 of 12). Our findings concerning the clinical history method are in good agreement with several previous

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studies11,25,28 in which the clinical history method obtained less accurate results than other methods, even when the calculated corneal power was entered into double-K formulas. Hence, we recommend extreme caution when using the corneal power generated by the clinical history method in any double-K formula and agree with Awwad et al.25 that this method should no longer be considered the gold standard for IOL power calculation after refractive surgery, at least in the real world. The Awwad method has not been evaluated in any study other than the original one, where it retrospectively provided excellent results in a sample of 30 eyes that had cataract surgery after myopic LASIK.25 Actually, Awwad et al.25 describe several equations in their paper, and we did not use the best one (ie, equation 1) because it relies on the average central corneal power measured by the TMS corneal topographer, which may not be available in all clinical settings. Rather, we preferred to adopt equation 2, which relies on simulated K. The results were poor using the double-K SRK/T. However, a remarkable improvement could be observed when the values of Awwad et al.’s method were entered into the double-K Holladay 1 rather than the double-K SRK/T formula. This is not surprising because Awwad et al. back-calculated their equations from the double-K Holladay 1. Feiz et al.5 described a formula and a nomogram (based on the formula) to calculate the IOL power after excimer laser surgery, the former to be used when both preoperative corneal power and refractive change are known, the latter when only the refractive change is available. In the present study, both methods overestimated the IOL power in all study groups. Our results agree with those in many other studies that found a mean myopic outcome with both methods14,28,42 but are worse than those reported by Wang et al.11 for the formula and Feiz et al.51 for the nomogram. In contrast, Randleman et al.52 found a mean IOL power underestimation with both methods. We also observed that the prediction error of both methods was statistically related to the amount of refractive change. Hence, both methods can be considered fairly accurate when the refractive change is moderate (lower than 8.00 D). As in the case of the clinical history method, the most likely explanation for these discrepancies lies in the low accuracy of the reported refractive change, which translates into a low accuracy of IOL power prediction. Relying on the cornea bypass method would have led to unpredicted myopic outcomes in many eyes, especially in cases of higher myopic correction by laser. Errors in estimating and reporting the refractive change induced by laser are the most likely

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explanation for the poor results obtained in our study. In addition, the results may have been inaccurate because third-generation formulas for IOL power calculation have not been developed or tested to achieve myopic refractions as high as 8.00 D or more. Our results are worse than those reported in the original paper by Walter et al.18 and later by Fam and Lim,43 but are similar to those reported by Geggel28 and Randleman et al.52 The method described by Rosa et al.6 overestimated IOL power by 2.00 D or more in all study groups. These results confirm the findings in our previous theoretical investigation, where we hypothesized that a myopic outcome might be expected in more than 50% of patients.21 The results also agree with those reported in other studies,17,27 including a recent paper by Rosa et al.53 As previously reported,21,28 the Ferrara method calculated the lowest corneal power; the consequences were a considerable IOL power overestimation and the highest degree of myopic refraction after IOL implantation. Hence, we still believe that the variable refractive index method developed by Ferrara et al.10 requires further refinement before its clinical application can be safely recommended. To help ophthalmologists choose which methods they should rely on, we propose a modification of a previously published decision tree (Figure 1).21 Of course this decision tree will be reviewed when new data from a larger sample are available. The present study has limitations. First, the sample size was relatively small; for this reason, patient enrollment will continue indefinitely and the results will be presented when more eyes are included in all groups so that it will be possible to analyze Group 4 as well. Second, we calculated IOL power using the double-K versions of the SRK/T formula and, in selected cases, the Holladay 1 and Hoffer Q formulas. Different results might have been obtained with the Haigis formula,54 which calculates the ELP without being influenced by the postoperative corneal power. Third, when calculating the post-refractive-surgery corneal power, we did not include many methods requiring specific instrumentation, such as the equivalent K reading or the BESSt formula of the Pentacam system,22,25 the Haigis-L formula of the IOLMaster device,27 the total corneal power of the Galilei dualScheimpflug imaging systems (Ziemer Group), the total axial and optical power of the Orbscan system,23 or the methods described by Wang et al.,11 Maloney, and Awwad et al. (equation 1).25 Fourth, we did not enter optimized constants into the IOL power formulas; however, this would have been impossible given the number of IOL models and instruments used by several ophthalmologists participating in this study.

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In conclusion, we prospectively compared several methods used to calculate the IOL power after myopic excimer laser surgery and found that, when the preoperative corneal power and the refractive change are known, the most accurate results can be obtained by entering the corneal power calculated using the Seitz/Speicher method (with or without the modification by Savini) and the Savini method into the doubleK SRK/T formula. Alternatively, the Masket method can be relied on, as can the Shammas no-history method (whose values must be entered into the Shammas-PL formula). Good results can also be achieved by entering the corneal power of the Camellin/Calossi and Awwad methods into the double-K Holladay 1 formula. When data concerning the preoperative corneal power are lacking but the refractive change is known, the same methods still provide the best outcomes in IOL power prediction. REFERENCES 1. Holladay JT. Consultations in refractive surgery [comment]. Refract Corneal Surg 1989; 5:203 2. Hoffer KJ. Intraocular lens power calculation for eyes after refractive keratotomy. J Refract Surg 1995; 11:490–493 3. Seitz B, Langenbucher A. Intraocular lens power calculation in eyes after corneal refractive surgery. J Refract Surg 2000; 16:349–361 4. Speicher L. Intra-ocular lens calculation status after corneal refractive surgery. Curr Opin Ophthalmol 2001; 12:17–29 5. Feiz V, Mannis MJ, Garcia-Ferrer F, Kandavel G, Darlington JK, Kim E, Caspar J, Wang J-L, Wang W. Intraocular lens power calculation after laser in situ keratomileusis for myopia and hyperopia; a standardized approach. Cornea 2001; 20:792–797 6. Rosa N, Capasso L, Romano A. A new method of calculating intraocular lens power after photorefractive keratectomy. J Refract Surg 2002; 18:; 720–704 7. Haigis W. Corneal power after refractive surgery for myopia: contact lens method. J Cataract Refract Surg 2003; 29:1397– 1411; erratum, 1854 8. Aramberri J. Intraocular lens power calculation after corneal refractive surgery: double-K method. J Cataract Refract Surg 2003; 29:2063–2068 9. Shammas HJ, Shammas MC, Gabaret A, Kim JH, Shammas A, LaBree L. Correcting the corneal power measurements for intraocular lens power calculations after myopic laser in situ keratomileusis. Am J Ophthalmol 2003; 136:426–432 10. Ferrara G, Cennamo G, Marotta G, Loffredo E. New formula to calculate corneal power after refractive surgery. J Refract Surg 2004; 20:465–471 11. Wang L, Booth MA, Koch DD. Comparison of intraocular lens power calculation methods in eyes that have undergone LASIK. Ophthalmology 2004; 111:1825–1831 12. Ladas JG, Stark WJ. Calculating IOL power after refractive surgery [letter]. J Cataract Refract Surg 2004; 30:2458 13. Jarade EF, Tabbara KF. New formula for calculating intraocular lens power after laser in situ keratomileusis. J Cataract Refract Surg 2004; 30:1711–1715 14. Latkany RA, Chokshi AR, Speaker MG, Abramson J, Soloway BD, Yu G. Intraocular lens calculations after refractive surgery. J Cataract Refract Surg 2005; 31:562–570

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47. Ho J-D, Liou S-W, Tsai RJ-F, Tsai C-Y. Estimation of the effective lens position using a rotating Scheimpflug camera. J Cataract Refract Surg 2008; 34:2119–2127 48. Hoffer KJ. Biometry of 7,500 cataractous eyes. Am J Ophthalmol 1980; 90:360–368; correction, 890 49. Khalil M, Chokshi A, Latkany R, Speaker MG, Yu G. Prospective evaluation of intraocular lens calculation after myopic refractive surgery. J Refract Surg 2008; 24:33–38 50. Binkhorst RD. Intraocular lens power. Int Ophthalmol Clin 1979; 19(3):83–94 51. Feiz V, Moshirfar M, Mannis MJ, Reilly CD, Garcia-Ferrer F, Caspar JJ, Lim MC. Nomogram-based intraocular lens power adjustment after myopic photorefractive keratectomy and LASIK; a new approach. Ophthalmology 2005; 112: 1381–1387 52. Randleman JB, Foster JB, Loupe DN, Song CD, Stulting RD. Intraocular lens power calculations after refractive surgery: consensus-K technique. J Cataract Refract Surg 2007; 33:1892–1898 53. Rosa N, Capasso L, Lanza M, Borrelli M. Clinical results of a corneal radius correcting factor in calculating intraocular lens power after corneal refractive surgery. J Refract Surg 2009; 25:599– 603 54. Haigis W, Lege B, Miller N, Schneider B. Comparison of immersion ultrasound biometry and partial coherence interferometry for intraocular lens calculation according to Haigis. Graefes Arch Clin Exp Ophthalmol 2000; 238:765–773

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First author: Giacomo Savini, MD G. B. Bietti Eye Foundation–IRCCS, Rome, Italy