IOL Calculations in Short, Long, and Postrefractive Eyes

Transcription

1 IOL Calculations in Short, Long, and Postrefractive Eyes Ildamaris Montes de Oca, MD Sabite E. Gökce, MD Katie Hallahan, MD Li Wang, MD, PhD Douglas D. Koch, MD Intraocular lens (IOL) Calculations: Fundamentals IOL power calculation formulas fall into 2 major categories: regression formulas and theoretical formulas. Regression formulas are empiric formulas generated by averaging a large number of postoperative refractive results. The first theoretical formula, based on principles of geometric optics, was developed by Fedorov in 1967, by using keratometry and A-scan ultrasonography. 1 The most well known of the first-generation regression formulas is the SRK I (by Sanders, Retzlaff, and Kraff). The SRK I formula is well known for its simplicity and ease of use and can be calculated easily as, P ¼ A 0:9K 2:5L; where P is the IOL power for emmetropia, K is the corneal refractive power, L is the axial length, and A is the IOL-specific A-constant. Most regression formulas are now considered to be largely outdated, and modern theoretic formulas based on geometrical optics are used instead. The eye is considered a 2-lens system consisting of the IOL and cornea. All modern formulas require an estimation of effective lens position (ELP), the position that the IOL will sit in the eye, which is calculated differently by each formula based on axial length (AL), corneal power (K), and anterior chamber depth (ACD) in some formulas. The estimation of ELP remains the true empirical content in INTERNATIONAL OPHTHALMOLOGY CLINICS Volume 56, Number 3,

2 50 Montes de Oca et al every IOL calculation formula and improvements in IOL power calculation are the result of improvements in the predictability of the ELP. It is important to note, however, that all theoretical formulas have a regression element, as the portion of the formula used to calculate ELP for any given IOL model is refined based on prior outcomes. Finally, a new regression formula was developed by Hill 2 based on the concept of radial basis function. It shows great promise to match or exceed the best theoretical formulas. Accurate biometry is of vital importance in achieving a predictable postoperative refraction following cataract surgery. The greatest step forward in biometry measurement has been the switch from measuring AL using ultrasound to using light. The optical biometry devices use the principle of partial coherence interferometry, which uses a 780-mm light wave that has 8 to 9 times the resolution of a 10-MHz sound wave. Thus, optical biometry is reported to have high resolution and precision in measuring intraocular distances as compared with conventional ultrasound. 3 New optical biometers have expanded the parameters that can be measured, not only AL and keratometry, but also white-to-white (WTW), pachymetry, lens thickness (LT), aqueous depth, ACD, and retinal thickness. Aside from an improvement in the calculation of the IOL power, proposed advantages of optical biometry include the increased comfort for the patient and increased ease of measurement of axial eye length in patients with retinal detachment, posterior staphylomas, and silicone-filled eyes. The primary limitation of optical biometry is its inability to measure through dense cataracts and other media opacities that obscure the macula; approximately 10% of eyes cannot be accurately measured using the optical biometry due to such opacities or fixation difficulties. 4 AL, ACD, and Corneal Power Significance in IOL Calculation The accuracy of IOL calculations principally depends on 3 factors: the precision of the preoperative biometric data (AL, ACD, K, and LT), the accuracy of the IOL power calculation formulas, and IOL power quality (control by the manufacturer). 5 On the basis of previous study, 54% of the error was attributed to AL errors, 8% to corneal power errors, and 38% to errors in the estimation of the postoperative ACD, when a fixed ACD was used in the IOL calculations. 6 This has undoubtedly changed with the introduction of optical biometers, which has greatly improved the accuracy of AL measurements. It is now commonly thought that the major source of error is the estimation of ELP, which places the burden for accuracy on the IOL calculation formula. 7

3 IOL Calculations in Short, Long, LASIK/PRK/RK Eyes 51 AL For several years, ultrasound was the only technique by which the AL could be measured in clinical practice. With A-scan biometry, errors in AL measurement accounted for 54% of IOL power error when using 2-variable formulas. A measurement error of 0.1 mm in AL would result in a postoperative refractive error of 0.28 D. 6,8 Optical biometry has been shown to be significantly more accurate and reproducible and is rapidly becoming the prevalent methodology for the measurement of AL. Optical biometry, through noncontact means, emits an infrared laser beam that is reflected back to the instrument from the retinal pigment epithelium. When the reflected light is received by the instrument, the AL is calculated using a modified Michelson interferometer. Optical biometry gives the refractive AL rather than the anatomic AL. The retinal pigment epithelium is the end point of an optical measurement, whereas the internal limiting membrane is the end point of an ultrasonic measurement; thus, measurements taken by optical biometry are longer than those taken with ultrasound. Kiss et al 9 reported a mean difference in the measured AL obtained with optical biometry and immersion biometry of 0.22 mm. The use of the optical AL instead of ultrasound AL has improved significantly the refractive results of cataract surgery. 10 ACD The clinical definition of ACD in the normal phakic eye refers to the distance from the cornea to the anterior surface of the crystalline lens. Anatomically, ACD is often calculated from the posterior surface of the cornea, but in an optical context (A-scan biometers and the optical biometry), such as when discussing ACD in an IOL power formula, the distance is normally measured from the anterior surface of the cornea to the anterior surface of the crystalline lens (including the corneal thickness). 8 In some IOL power calculation formulas, the measured ACD is used to aid in the prediction of the final postoperative position of the IOL, ELP. Optical biometers use partial coherence interferometry to obtain accurate and reproducible ACD measurements. Corneal Power Corneal power accounts for about two thirds of the total dioptric power of the eye and is an essential factor of the ocular refractive system. If the calculation of corneal power is inaccurate, it will induce error and have significant consequences on the remaining steps in the calculation of IOL power. 8 A 0.50 D error in keratometry will result in approximately a 0.50 D postoperative error at the spectacle plane. Currently, different technologies are available to measure K, including manual keratometry, automated keratometry, and corneal topography. These devices measure the radius of curvature and provide the K value in the form of keratometric diopters using an assumed index of refraction of The principle behind the keratometry measurement is that the central cornea is assumed to be a perfect sphere and acts

4 52 Montes de Oca et al as a spherical convex mirror. The contribution of posterior corneal curvature to the total refractive power of cornea is assumed to be limited and fixed; due to which increased errors are observed after refractive surgeries. From the size of the reflected image from the cornea acting as a convex mirror, the radius of curvature is determined. Two of the most commonly used optical biometers measure the cornea with different algorithms. The IOLMaster (Carl Zeiss, Jena, Germany) measures keratometry at a 2.5 mm ring, whereas the Lenstar (Haag Streit, Koeniz, Switzerland) takes 2 sets of keratometric readings at 1.65 mm and 2.3 mm and combines them through an iteration process for improved consistency. Although some studies observed significant differences between K readings assessed with different optical biometry devices, these differences are small and may be considered clinically insignificant. 11 The obtained measurements should be compared with the patient s manifest refraction, looking for large inconsistencies in the magnitude or meridian of the corneal astigmatism that could indicate the need for further evaluation of the accuracy of the corneal readings. Accurate estimation of K is difficult, if not impossible, in the presence of corneal scars or dystrophies that create an irregular anterior corneal surface. Although these lesions can often be seen with slit-lamp biomicroscopy, their effect on K measurements can best be assessed by examining keratometric or topographic Placido disc mires. The latter in particular give an excellent qualitative estimate of corneal surface irregularity. Treatment of these lesions before cataract surgery is usually indicated and can improve both the accuracy of IOL calculations and quality of postoperative vision. Examples would include epithelial debridement in corneas with epithelial basement membrane disease, and superficial keratectomy in eyes with Salzmann s nodular degeneration. If the patient has undergone prior corneal refractive surgery, or corneal transplantation, standard keratometric and topographic measurements cannot be used. This topic will be further discussed below. The Second, Third, and Fourth Generation Available Formulas The A-constant of the first-generation SRK I formula was further modified into 6 subgroups depending on the AL: increasing the A- constant for short eyes and decreasing the A-constant for long eyes. The result was the SRK II formula, which emerged as a second-generation formula. Predictability improved markedly when compared with firstgeneration formula, but spectacle correction was still necessary for most patients. 12 The third-generation formulas, Holladay I, Hoffer Q, and the SRK/T, aimed to predict postoperative ACD or ELP more accurately by incorporating the effect of the corneal curvature. All 3 formulas are

5 IOL Calculations in Short, Long, LASIK/PRK/RK Eyes 53 basically similar, and they all require knowledge of AL and K. Other than the lens constant specific to each formula, the shape of the power prediction curve is mostly fixed. The IOL constants of these formulas work by simply moving up or down the position of an IOL power prediction curve. Commonly used lens constants are: SRK/T formula uses an A-constant. Holladay 1 formula uses a Surgeon Factor. Hoffer Q formula uses a Pseudophakic Anterior Chamber Depth (pacd). These standard IOL constants are mostly interchangeable; surgeons can estimate one by knowing another and can move from one formula to another for the same IOL implant. The Holladay 1 and SRK/T formulas use the Fedorov et al 1 corneal height equation to predict postoperative ACD, whereas the Hoffer Q formula uses an independently developed formula in which the tangent of corneal power is used. 13 These formulas treat all IOLs the same and make a number of broad assumptions for all eyes regardless of individual differences. Variations in keratometers and surgical techniques (such as the creation of the capsulorhexis) can impact the refractive outcome as independent variables. Personalizing the lens constant for a given IOL and formula can be used to make global adjustments for a variety of practice-specific variables. The latest fourth-generation formulas use additional biometric parameters such as ACD, LT, WTW, preoperative refraction, etc. Although the third-generation and fourth-generation formulas agree for most eyes, in unusual circumstances there can be greater accuracy with the newer formulas. The Haigis formula attempts to treat each IOL as an individual entity. It uses a function consisting of 3 constants (a 0,a 1, and a 2 ) to set both the position and the shape of the IOL power prediction curve instead of simply moving a fixed IOL power prediction curve up (more IOL power recommended) or down (less IOL power recommended). d ¼ a 0 þða 1 ACDÞþða 2 ALÞ; where d is the effective lens position, ACD is the measured anterior chamber depth of the eye (corneal vertex to the anterior lens capsule), and AL is the axial length of the eye (corneal vertex to the vitreoretinal interface). The a 0 constant acts in much similar way as the A-constant, Surgeon Factor, or pacd acts for the SRK/T, Holladay 1, and Hoffer Q formulas, respectively, moving the power prediction curve up or down. The a 1 constant is tied to the measured ACD, and changes the shape of the

6 54 Montes de Oca et al outcome curve. The a 2 constant is tied to the measured AL, and it also changes the shape of the outcome curve. As a consequence, the value for ELP (d) is determined by 3 constants, rather than a single constant. By regression analysis, a 0,a 1, and a 2 constants are calculated to individually adjust the IOL power prediction curve for each surgeon/iol combination in such a way to closely reproduce observed results over a wide range of ALs and ACDs. The Holladay 2 formula uses measurements of corneal power, WTW, ACD, LT, preoperative refractive error, AL, and age to further refine the ELP calculation. The Holladay 2 formula is based on previous observations from a large research data set and has been shown to be particularly advantageous in short eyes. The Olsen formula uses a new C-constant that describes the IOL position as a constant fraction of the LT with good results. 14 The Barrett Universal II formula is based on paraxial ray tracing and takes into account the change in the principle planes encountered with different powered IOLs. It uses 5 variables consisting of AL, Ks, ACD, LT, and WTW. 15 IOL Power Calculation in Short Eyes Theoretical Considerations Regarding Optimal Formulas for Calculating IOL Power in Short Eyes Modern IOL power calculation formulas show accurate refractive outcomes in eyes with an average AL. However, in eyes with short ALs, refractive accuracy of the formulas differs The prediction of pseudophakic ACD is a critical step, and the inability to accurately predict ELP remains a major source of error in IOL power calculations. This problem is magnified in short eyes due to the high power of the IOL and the relatively short distance from the IOL to the retina. Olsen 8 showed that 0.25 mm error in postoperative ACD corresponds to a 0.1 D error in a 30 mm long eye and a 0.5 D error in a 20 mm short eye. It is accepted that postoperative ACD is strongly correlated with AL. Popular third-generation 2-variable formulas (SRK/T, Hoffer Q, and Holladay 1) use this assumption and relate the distance between the principal plane of the cornea and the thin lens equivalent of the IOL, ELP, to the AL. This prediction is accurate for most eyes within the normal range, but errors may arise in short eyes. In those formulas that do not use ACD measurements in the ELP calculation, it is assumed that short eyes have a proportionally shallower anterior chamber. However, this assumption breaks down in the many short eyes that in fact have perfectly normal anterior chamber anatomy with normal ACD. This assumption error accounts for the characteristic AL limited accuracy of each third-generation 2-variable formula.

7 IOL Calculations in Short, Long, LASIK/PRK/RK Eyes 55 The so-called fourth-generation (Haigis, Holladay 2) and fifthgeneration formulas (Olsen and Barrett Universal II) are proving to be superior for short eyes as they calculate ELP using ACD (Haigis) or using both ACD and LT (Holladay 2, Olsen, and Barrett Universal II). Accuracy of Different Formulas in Short Eyes There are several studies in the literature that compare different IOL power calculation formulas and their accuracy in short eyes (Table 1). The most recent study by Carifi et al 24 showed only a statistically nonsignificant trend toward better accuracy with the Holladay 2, the Haigis, and the Hoffer Q formulas against the Holladay 1 and the SRK/T formulas in short eyes. Although it is believed that the latest generation IOL power prediction formulas would perform best in short eyes, there is still uncertainty in the literature on whether any of the available formulas would perform better than the others. Our personal experience suggest that the Olsen and Barrett formulas are particularly helpful for short eyes, as they effectively factor in ACD and LT in their prediction of ELP. However, in some hyperopic eyes with shallow anterior chambers, the IOL sits more anteriorly that predicted by even these formulas, producing postoperative myopia. We now routinely warn patients of this possibility. The nanophthalmic eye is the extreme case of the short eye, and calculations in these eyes are particularly problematic due to the uncertainty of ELP and the high power of the IOL. A recent study showed that the refractive predictability and postoperative outcome was poorer in eyes with nanophthalmos compared with eyes with relative anterior microphthalmos or normal controls, and the Holladay 1 formula produced the best refractive results when compared with SRK II, SRK/T, and Hoffer Q formulas, as measured by mean numeric error. 25 In general, our approach for short eyes is to use the Holladay 1, Olsen, and Barrett, favoring the Olsen when there is disagreement. We also try to operate on the nondominant eye first so that we can use its refractive outcome to adjust the IOL power for the second eye, generally changing the calculated IOL power by one half of the prediction error in the first eye. IOL Power Calculation in Long Eyes Optimizing IOL Power Calculation in Long Eyes IOL power formulas tend to select IOLs of insufficient power in long eyes, leaving patients with postoperative hyperopia To reduce the chance for hyperopic surprises, many surgeons empirically aim for a more

8 56 Montes de Oca et al Table 1. References Summary of Studies on Formula Choice in Short Eyes No. Eyes AL (mm) Formulas Used Results Gavin and 41 <22.0 Hoffer Q and SRK- Hammond 16 T Narvaez et al <22.0 Hoffer Q, Holladay 1, Holladay 2, and SRK/T Terzi et al <22.0 Holladay 2, Hoffer Q, SRK/T, and Haigis MacLaren et al <22.95 (only 1 eye>22.0) Hoffer Q, SRK/T, Haigis, and Holladay 1 Eom et al <22.0 Hoffer Q and Haigis Roh et al <22.0 Haigis, Hoffer Q, SRK II, and SRK/T Wang and 33 <22 Haigis, Hoffer Q, Chang 22 Holladay 1, SRK/T Aristodemou 457 <22.0 Hoffer Q, Holladay et al 23 1, SRK/T Carifi et al <20.9 Hoffer Q, Holladay 1, Holladay 2, Haigis, SRK/T and SRK-II Hoffer Q formula was significantly more accurate than the SRK-T No difference in the accuracy of IOL power prediction with the Hoffer Q, Holladay 1, Holladay 2, and SRK/T No statistically significant differences in MAE values between the formulas Haigis formula showed the best MAE and MPE No significant difference between the MedAEs of Hoffer Q and Haigis when ACD is >2.4 mm. When ACD is <2.4 mm Hoffer Q produced more hyperopic correction No statistically significant difference among formulas except Haigis vs. SRK II Haigis and Hoffer Q yielded comparable results, both performing better than the Holladay 1 and SRK/T formulas The Hoffer Q performed best for ALs from to mm, the Hoffer Q and Holladay 1 for ALs from to mm Not statistically significant trend toward better results with Holladay 2, Haigis and Hoffer Q formulas MAE indicates mean absolute error; MedAE, median absolute error; MPE, mean prediction error.

9 IOL Calculations in Short, Long, LASIK/PRK/RK Eyes 57 myopic postoperative outcome by targeting a postoperative refraction of 1.00 to 2.00 D. Several authors have reported outcomes of various formulas for calculating IOL power in long eyes. The trend in these studies was that the Haigis tended to be more accurate than the Holladay 1 and 2, Hoffer, and SRK-T (Table 2). However, accuracy was still suboptimal, as the best outcomes still showed around 60% to 80% with hyperopic outcomes (mean absolute errors within ± 1.0 D). An important breakthrough occurred with a new approach: optimize the AL instead of the lens constant. In a study by PreuXner et al, 33 the following equation was used to transform the AL values given by the IOLMaster: Transformed AL = IOLMaster AL This transformation reduced the AL values and gave zero prediction error and zero steepness of the regression line fitted to the prediction error. Wang et al 34 developed a method of optimizing AL to improve the prediction accuracy. In their comprehensive analysis, they suggest that AL measurements are the primary source of suboptimal outcomes. They proposed optimizing AL in eyes with AL>25.2 mm. For IOLs of Z6.0 D, the performance of optimizing AL was comparable with that of optimizing lens constants. However, for IOLs of r5.0 D, the best results were obtained with the optimized AL values combined with the manufacturer s lens constants, both in terms of mean accuracy and a much smaller SD. They recommend caution when using the optimized AL formulas as slightly myopic results may occur. They aim for slight myopia of approximately 0.1 to 0.2 D in these eyes. The Wang-Koch adjustment is more aggressive than that of PreuXner, reducing the likelihood of hyperopic surprises. The updated equations of optimizing AL are as follows 34 (Table 3). IOL Power Calculation Formulas in Long Eyes A recent advance has been the development of the Barrett Universal II formula, which has been refined to improve outcomes in long eyes. In recent study of eyes 26.0 mm and longer, Abulafia et al 35 compared the results of Haigis, Holladay 2, Olsen, and Barrett Universal II as well as SRK/T, Holladay 1, Hoffer Q, and Haigis formulas using the Wang-Koch adjustment. For IOL powers Z6.0 D, lowest mean absolute errors were seen with the SRK/T, Haigis, Barrett Universal II, Holladay 2, and Olsen formulas, whereas for IOL powers <6 D, best results occurred with the Holladay 1with AL adjustment, Haigis with AL adjustment, and Barrett Universal II formulas. A pleasant surprise has been the now obvious recognition that IOL calculations in long eyes have 1 advantage: ELP is not as important as in normal and short eyes, due to the low IOL power. By refining the AL value used in current formulas, excellent outcomes can be anticipated as shown in Wang s and Abulafia et al s studies. 34,35

10 58 Montes de Oca et al Table 2. Outcomes of Studies That Compared IOL Lens Power Calculation Formulas in Eyes With Long Axial Length References No. Eyes AL (mm) Formulas Used Results Narvaez 643 Short: <22.0 et al 17 Average: 22.0-<24.5 Medium long: Very long: >26.0 Wang and Chang Group 1: <22.0 Group 2: Group 3: >26.0 Holladay 1, Holladay 2, SRK/T, and Hoffer Q Holladay 1, SRK/T Haigis, and Hoffer Q The 4 formulas were equally accurate at all axial lengths Haigis and SRK/T performed best for long eyes. All formulas were equally good for medium eyes Abulafia et al >26.0 Haigis, Holladay 2, Olsen, and Barrett Universal II. SRK/T, Holladay 1, Hoffer Q, and Haigis (using the Wang-Koch adjustment) Best results were seen: IOL powers Z6.0 D: SRK/T, Haigis, Barrett Universal II, Holladay 2, and Olsen. IOL powers < 6 D: Barrett Universal and Holladay 1, Haigis with AL adjustment Hoffer Short: <22.0 Average: Medium long: Very long: >26.0 Holladay 1, Holladay 2, SRK/T, and Hoffer Q Wang 68 >25.0 Holladay 1, SRK/T et al 35 Haigis, and SRK II Bang 53 >27.0 Holladay 1, Holladay 2, et al 36 SRK/T Hoffer Q and Haigis Holladay 1 was the best for average and medium long eyes ( mm). SRK/ T showed a trend toward better results in very long eyes Haigis formula yielded a better outcome in eyes with AL >25.0 mm Haigis formula most accurate followed by Holladay 2, Holladay 1, and then the Hoffer Q IOL Power Calculation for Eyes With Prior Corneal Refractive Surgery Special consideration should be given to calculating the IOL power for eyes that have undergone prior corneal refractive surgery. Ablative

11 IOL Calculations in Short, Long, LASIK/PRK/RK Eyes 59 Table 3. Updated Equations for Axial Length Optimization 34 Combining All Eyes From 1 Study Center (n = 200) Holladay 1 1-center optimized AL = IOLMaster AL Haigis 1-center optimized AL = IOLMaster AL SRK = T 1-center optimized AL = IOLMaster AL Hoffer Q 1-center optimized AL = IOLMaster AL Combining All Eyes From 2 Study Centers (n = 222) Holladay 1 2-center optimized AL = IOLMaster AL Haigis 2-center optimized AL = IOLMaster AL SRK = T 2-center optimized AL = IOLMaster AL Hoffer Q 2-center optimized AL = IOLMaster AL procedures can introduce error to the IOL power calculation in several ways. First, the measurement of anterior corneal curvature by standard keratometry or computerized videokeratography becomes inaccurate because these methods measure a paracentral region and assume that this accurately reflects central corneal power. Second, in the calculation of total corneal power (TCP), the assumption that there is a normal relationship between the anterior and posterior corneal curvatures no longer applies. In turn, central corneal power may be underestimated in eyes following myopic ablation and overestimated in eyes following hyperopic ablation. Finally, postrefractive surgeries can lead to an incorrect estimation of ELP by the third-generation or fourth-generation formulas, with the exception of the Haigis formula, when the postoperative corneal power values are used. 39,40 To correct for inaccurate ELP, one may choose the following: (1) substitute D as the default preoperative corneal value if using the double K feature of the Holladay 2 formula and preoperative corneal power is unknown; (2) apply Aramberri s 39 double-k method correction to the Holladay 1, Hoffer Q, or SRK/T formulas; or (3) refer to the IOL power adjustment nomograms published by Koch and Wang. 40 Despite the challenges previous refractive surgery has on postoperative refraction predictability, multiple approaches to choosing an IOL power in these cases have been developed and continue to be refined. Broadly, methods for determining IOL power in postcorneal refractive surgery eyes fall into 3 groups: (1) those that rely on historical data and ignore corneal measurements at the time the patient presents for surgery, (2) those that use the ablation-induced change in refraction to adjust either corneal or IOL power, and (3) those that rely solely on measurements obtained when the patient presents for surgery. Methods Requiring Historical Data for Corneal Power and Change in Refraction Clinical History Method 41 If one knows accurate historical data, the clinical history method can be used for corneal power estimation:

12 60 Montes de Oca et al K p þse p SE a ¼ K a ; where K p is the average keratometry power before corneal refractive surgery, SE p is the spherical equivalent before corneal refractive surgery, SE a is the stable spherical equivalent after corneal refractive surgery, and K a is the estimate of the central corneal power after corneal refractive surgery. Feiz-Mannis IOL Power Adjustment Method 42 With this method, the IOL power is first calculated using the prelaser in situ keratomileusis (pre-lasik) corneal power, which is then increased by the amount of refractive change at the spectacle plane divided by 0.7: IOLpreþ DD=0:7 ¼ IOLpost; where IOLpre is the power of the IOL as if no LASIK had been performed, DD is the refractive change after LASIK at the spectacle plane, and IOLpost is the estimated power of the IOL to be implanted following LASIK. Despite the theoretical appeal of these clinical history methods, we recently removed them from the ASCRS Post-Refractive IOL Calculator due to the much worse accuracy compared with the approaches noted below. Sources of error are numerous and can directly affect IOL selection on a diopter-to-diopter basis, including inaccurate preoperative keratometer (technician error, poor calibration, nonzeroed eyepiece), inaccurate preoperative or postoperative refraction, and any ongoing changes in corneal curvature that might have occurred. Methods Using Historical Data Refractive Change Induced by Surgery to Modify Corneal or IOL Power Topographic Corneal Power Adjustment Method Multiple methods that modify topographic acquisition of postrefractive corneal power measurements have been described. To adjust the effective refractive power (EffRP) of the Holladay Diagnostic Summary of the EyeSys Corneal Analysis System, the following formulas after myopic 43 or hyperopic surgery 44 may be used, respectively: EffRP ðdd0:15þ 0:05 ¼ postmyopic LASIK adjusted EffRP EffRP ðdd0:16þ 0:28 ¼ posthyperopic LASIK adjusted EffRP; where DD is the refractive change after LASIK at the spectacle plane. To average the corneal curvatures of the center and the 1, 2, and 3 mm annular rings from the Zeiss Atlas topographer (AnnCP) and modify the

13 IOL Calculations in Short, Long, LASIK/PRK/RK Eyes 61 result, use the following formula 44 : AnnCPþðDD0:19Þ 0:4 ¼ posthyperopic LASIK adjusted AnnCP: To use the Atlas mm zone value from the Zeiss Atlas 9000 topographer and modify the result according to the amount of refractive correction induced by the surgery 45 :Atlas mm zone (DD 0.2) = post-lasik/photorefractive keratectomy (PRK) adjusted corneal power. To obtain the average central corneal power (ACCP) through the Tomey Topography Modeling System, one averages the mean powers of the central Placido rings over the central 3 mm of the cornea and modifies the result 46 : ACCP ðdd0:16þ ¼ postlasik=prk adjusted corneal power: To modify keratometry (K) values, though note that this method is not as accurate as the topography-based methods above 43 : K ðdd0:24þþ0:15 ¼ postmyopic LASIK adjusted K: Masket IOL Power Adjustment Method 47 The Masket IOL power adjustment method comes from a regression analysis and modifies the predicted IOL power obtained by using the patient s postablation correction readings: IOLpostþðDD0:326Þþ0:101 ¼ IOLadj; where IOLpost is the calculated IOL power following ablative corneal refractive surgery, DD is the refractive change after corneal refractive surgery at the spectacle plane, and IOLadj is the adjusted power of the IOL to be implanted. A modified version of this formula that attempts to increase the accuracy of IOL power prediction has also been presented 48 : IOLpostþðDD0:4385Þþ0:0295 ¼ IOLadj: Barrett True-K IOL Power Adjustment Method 49 The Barrett True- K formula takes into account the refractive change induced by the refractive surgery. For IOL power calculation, the Universal II formula is used; this is a modification of the original universal theoretic formula. 50,51 Details regarding these formulas remain unpublished, but an online calculator to obtain IOL power can be accessed from the Asia Pacific Association of Cataract and Refractive Surgeons (APACRS) ( and American Society of Cataract and Refractive Surgery (ASCRS) ( Web sites.

14 62 Montes de Oca et al Methods Requiring No Historical Data Often, patients present to the clinician with no knowledge or record of their prerefractive surgery topographic or biometric data, refraction, or ablation profile. For these cases, the development of accurate methods to calculate IOL power without historical data is crucial. Hard Contact Lens Overrefraction Method This method can only be used if the visual acuity is better than 20/80 52 and uses the following formula: B c þp c þse c SE s ¼ K a ; where B c is the base curve of contact lens in diopters, P c is the refractive power of contact lens in diopters, SE c is the spherical equivalent with contact lens in place, SE s is the spherical equivalent without contact lens, and K a is the estimated corneal power following refractive surgery. It should be noted that studies suggest this method to be less accurate than originally thought and thus is not the preferred method for IOL power calculation following ablative corneal refractive surgery where no prior historical data are known. 45,53 55 Although this method is theoretically appealing, it is rarely used, in part, because of the challenge of obtaining a good contact lens fit for the evaluation. Wang-Koch-Maloney Method 45 This technique modifies a method of post-lasik corneal power estimation that was originally described by Robert Maloney. The central corneal power is obtained by placing the cursor at the exact center of the Axial Map of the Zeiss Atlas topographer. This value is then converted back to the anterior corneal power by multiplying this value by 376.0/337.5 or An assumed posterior corneal power of 6.1 D is then subtracted from this product: ðccp1:114þ 6:1D¼ postlasik adjusted corneal power; where CCP is the corneal power with the cursor in the center of the topographic map. This method was found to have a low variance when used with either the Holladay 2 formula or a modern third-generation 2-variable formula combined with the double-k method correction nomogram. 40 Shammas Clinically Derived IOL Power Adjustment Method 56,57 This method uses a regression analysis to estimate the post-lasik/prk corneal power by adjusting K readings obtained from the IOLMaster: 1:14Kpost 6:8 ¼ PostLASIK PRK corneal power ;

15 IOL Calculations in Short, Long, LASIK/PRK/RK Eyes 63 where Kpost is the average postrefractive procedure K value from the IOLMaster. The IOL power is then calculated using the Shammas-PL formula instead of the Holladay 1 double-k formula. 57 Haigis-L IOL Power Adjustment Method 58 Using the IOLMaster to measure the corneal radius, a corrected corneal radius is calculated: r corr ¼ 331:5 ð 5:1625r measþ82:2603 0:35Þ ; where r meas is the corneal radius in mm as measured by the IOLMaster and r corr is the corrected corneal radius. This is then substituted into the regular Haigis formula to calculate IOL power following myopic laser vision correction. Galilei TCP Method The Galilei TCP represents the average TCP for the central 4 mm diameter of the cornea. It is calculated using the ray tracing method that takes into account the actual refractive indices of the cornea. Using a regression analysis that compared Galilei data to historical method results, the post-lasik/prk corneal power formula follows (unpublished data from Koch DD, Wang L; 2008): 1:057TCP 1:8348 ¼ PostLASIK PRK adjusted corneal power : Potvin-Hill IOL Power Adjustment Method 59 Using regression analysis, this formula estimates the post-lasik/prk corneal power using Pentacam data, AL and the ACD, if available. If ACD is unknown: K c ¼ 12:08þð0:9true net power apex zone40þ 0:282AL; where K c is the corrected K value. true_net_power_apex_zone40 = true net corneal power in the central 4 mm of the cornea, centered on the corneal apex, as reported by the Pentacam. AL is the axial length. If ACD is known: K c ¼ 11:19þð0:951true net power apex zone40þ ð0:247alþð0:588acdþ: For IOL power calculation, the Shammas-PL formula is used. 57 Optical Coherence Tomography (OCT)-based IOL Power Calculation Method With the introduction of OCT, the accuracy of direct measurements of corneal power theoretically improves compared

16 64 Montes de Oca et al with slit-scanning tomography, rotating-slit Scheimpflug camera, and dual-scheimpflug systems. In slit-scanning devices, the axial resolution ranges from 50 to 100 mm, whereas OCT axial resolution spans 3 to 17 mm in commercially available instruments. 60 This allows for clear delineation of corneal boundaries and eliminates errors related to the presence of corneal haze or opacities. 61 Corneal mapping speed also improves with OCT over slit-scanning instruments. 60 The OCT-based IOL formula is based on vergence tracing from the retinal plane to the anterior corneal surface. 62 It takes into account the following: AL and ACD (distance from corneal epithelium to the crystalline lens) from the IOLMaster, net corneal power, posterior corneal power, and central corneal thickness from the OCT (RTVue or RTVue-XR). Net corneal power is calculated using the Gaussian thick lens formula. For calculation of the IOL power, an effective corneal power is derived based on linear regression analysis: Effective corneal power in postmyopic LASIK=PRK ¼ 1:0208net corneal power 1:6622: It is recommended to perform 3 OCT scans and use the median net and posterior corneal power for best results. Barrett True-K-No History IOL Power Adjustment Method 49 As its name implies, the Barrett True-K-No history formula does not require prerefractive surgery clinical data for IOL power calculation. Like the Barrett True-K formula, details of its derivation remain unpublished. For IOL power calculation, the Universal II formula is again used. 50,51 The IOL power calculator for the Barrett True-K-No history formula can also be accessed from the APACRS ( and ASCRS ( Web sites. Prior Hyperopic Corneal Refractive Surgery If not already explicitly delineated in the preceding sections, many of the above formulas also apply to prior hyperopic ablation treatments. In fact, for eyes that have undergone hyperopic ablation, it is often easier to estimate central corneal power because the ablation takes place outside the central cornea. For example, the average of the 0, 1, 2, and 3 mm annular power rings from the Zeiss Atlas topographer can serve as an estimate of central corneal power following hyperopic LASIK. As an alternative, the adjusted EffRP of the EyeSys Corneal Analysis System may also be used. In general, some form of a double-k method is still required for IOL power calculations following hyperopic LASIK to avoid an inaccurate estimation of ELP. Head-to-head comparisons of the above methods have been performed in a limited number of studies. Newer formulas generally

17 IOL Calculations in Short, Long, LASIK/PRK/RK Eyes 65 outperformed older methods that depend on historical data. For example, Wang et al 63 found that methods using surgically induced change in refraction or no previous data had significantly smaller mean absolute IOL predictive errors, smaller variances, and a greater percentage of eyes within 0.5 D of refractive prediction errors than methods using pre-lasik/prk keratometry and surgically induced change in refraction. Likewise, a large case series of 104 eyes with prior myopic LASIK or PRK undergoing cataract surgery observed similar results. They found that the OCT-based formula produced the smallest variance of IOL predictive error and the smallest median absolute refractive predictive error, followed by Haigis-L and Barrett True-K-No history, though there were no significant differences between these groups. When compared with older methods such as the Wang-Koch- Maloney and Shammas formula, the OCT method had significantly smaller variances of IOL predictive error. Similar results were found when comparing the OCT-based formula to a subgroup using EffRP, Adjusted Atlas, Masket, and the modified Masket formulas. 49 Larger studies with extended follow-up should be conducted as additional methods for IOL power calculation develop. Newer intraoperative technology can also help in determining IOL power calculation for eyes with previous laser vision correction. Intraoperative wavefront aberrometry, such as the Optiwave Refractive Analysis (ORA) system (Wavetec Vision Systems Inc, Aliso Viejo, CA), may have advantages over preoperative methods of IOL power prediction because it measures an aphakic refraction at the time of cataract surgery. For example, because it uses infrared laser that is reflected off the retina, it can account for the refractive state of the entire optical media. It also takes into account surgically induced corneal changes that would not be apparent preoperatively. Studies directly comparing this technology to conventional IOL power calculation methods are limited but show promising results. In a large retrospective series of 215 eyes, ORA showed the greatest predictive accuracy compared with surgeon best choice using all clinical data, the Haigis-L method, and Shammas formula. With ORA, 67% of eyes were within 0.50 D of their predictive refractive outcome. 64 Likewise, other studies have shown that mean predictive error was smaller or not significantly different when intraoperative aberrometry was used compared with the ASCRS calculator, Haigis-L formula, Masket regression formula, or OCT formula. 65,66 Future studies with larger sample sizes and a prospective design are needed to further evaluate the advantages of intraoperative aberrometry. Research should also improve current factors that limit its accuracy such as dependence on patient fixation, intraocular pressure, and corneal thickness.

18 66 Montes de Oca et al Prior Radial Keratotomy Radial keratotomy causes a flattening of both the anterior and posterior corneal radii, and thus, unlike the ablative forms of corneal refractive surgery, the ratio between the anterior and posterior radii is generally preserved. This allows for direct measurement of the central corneal power, and, thus, any map that provides some average of anterior corneal power over the central 2 to 3 mm gives an accurate estimation of corneal refractive power. For example, one may use the EffRP from the Holladay Diagnostic Summary of the EyeSys Corneal Analysis system, the central annular rings or zone values from the Zeiss Atlas topographer, central Pentacam data, or OCT-derived corneal power. Again, potential errors in ELP must still be taken into account by using the Holladay 2 formula or the double-k approach with thirdgeneration formulas, as previously described. Of note, transient hyperopia, as high as D, in the immediate postoperative period following cataract surgery can occur in patients with previous radial keratotomy. 67 This may be due to stromal edema around the radial incisions, which flattens the central cornea, and is more likely to occur in eyes with Z8 incisions, an optical zone of <2.0 mm, or incisions that extend to the limbus. The hyperopia may take 8 to 12 weeks to resolve. Thus, it is recommended to follow these patients closely before surgical intervention to correct postcataract surgery refractive errors. Likewise, IOL power calculations may benefit from a more myopic target, around 1.00 D. Generally, predictions for eyes after radial keratotomy were worse than those who had previous ablation procedures. 68 ASCRS Online Calculator In order for clinicians to conveniently use the above methods to determine IOL power in postcornea refractive surgery eyes, an online IOL power calculator is available at the ASCRS Web site ( This calculator has 3 modules for eyes with prior myopic LASIK or excimer laser PRK, hyperopic LASIK/PRK, or radial keratotomy. Version 4.7 of the calculator was updated in 2015 and eliminates methods that depend entirely on historical data due to their decreased accuracy. It does, however, include more recent methods such as the Barrett True-K formula, OCT-based formula, and the Potvin-Hill Pentacam method. The IOL calculator is intended to serve as an adjunct tool in selecting the appropriate IOL for a particular patient, in conjunction with a comprehensive ophthalmic examination and necessary ancillary tests.

19 IOL Calculations in Short, Long, LASIK/PRK/RK Eyes 67 Conclusions Methods for accurately calculating IOL power in normal and complex eyes are constantly evolving. Studies should continue to investigate how to best measure biometric data such as corneal power, AL, and ACD and how to accurately predict ELP. Future advances in IOL design and postoperative modification may also contribute to the goal of eliminating postoperative refractive error and meeting patient expectations in cataract surgery. L.W. received research support from Ziemer USA Inc. D.D.K. is a consultant to Alcon Laboratories Inc. and Abbott Medical Optics Inc., and received research support from Ziemer USA Inc., i-optics Corp, and True Vision Systems. The other authors declare that they have no conflicts of interest to disclose. References 1. Fedorov SN, Kolinko AI, Kolinko AI. Estimation of optical power of the intraocular lens. Vestn Oftalmol. 1967;80: Hill WE, Charles D. Kelman Lecture IOL Power Selection: Think Different. Las Vegas: American Academy of Ophthalmology; Findl O, Drexler W, Menapace R, et al. High precision biometry of pseudophakic eyes using partial coherence interferometry. J Cataract Refract Surg. 1998;24: Lege BA, Haigis W. Laser interference biometry versus ultrasound biometry in certain clinical conditions. Graefes Arch Clin Exp Ophthalmol. 2004;242: Drexler W, Findl O, Menapace R, et al. Partial coherence interferometry: a novel approach to biometry in cataract surgery. Am J Ophthalmol. 1998;126: Olsen T. Sources of error in intraocular lens power calculation. J Cataract Refract Surg. 1992;18: Findl O. Biometry and intraocular lens power calculation. Curr Opin Ophthalmol. 2005;16: Olsen T. Calculation of intraocular lens power: a review. Acta Ophthalmol Scand. 2007;85: Kiss B, Findl O, Menapace R, et al. Refractive outcome of cataract surgery using partial coherence interferometry and ultrasound biometry: clinical feasibility study of a commercial prototype II. J Cataract Refract Surg. 2002;28: Connors R, Boseman P, Olson RJ. Accuracy and reproducibility of biometry using partial coherence interferometry. J Cataract Refract Surg. 2002;28: Hoffer KJ, Shammas HJ, Savini G. Comparison of 2 laser instruments for measuring axial length. J Cataract Refract Surg. 2010;36: Dang MS, Raj PP. SRK II formula in the calculation of intraocular lens power. Br J Ophthalmol. 1989;73: Hoffer KJ. The Hoffer Q formula: a comparison of theoretic and regression formulas. J Cataract Refract Surg. 1993;19: Errata 1994; 20: Olsen T. Prediction of the effective postoperative (intraocular lens) anterior chamber depth. J Cataract Refract Surg. 2006;32:

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