IOL Power Calculations for Postrefractive Surgery Eyes

Transcription

1 eyetube.net The Creator s Forum: IOL Power Calculations for Postrefractive Surgery Eyes The minds behind today s commonly used formulas provide overviews and pearls for use. By Wolfgang Haigis, Ms, PhD; Kenneth J. Hoffer, MD; Jack T. Holladay, MD; and Thomas Olsen, MD, phd Haigis-L Formula By Wolfgang Haigis, MS, PhD With its three constants a0, a1, and a2 properly optimized, the regular Haigis formula has a good and proven clinical performance irrespective of axial length (AL). 1 Because corneal power is not used in this formula as a predictor of the effective lens position (ELP), it has the advantage that, for application after refractive surgery, only the keratometer index error must be corrected. By comparing measurement results of the IOLMaster (Carl Zeiss Meditec) with those from the refractive history method with reliable data, 2,3 a correction curve for the IOLMaster was derived. This curve translates the keratometric measurements of the IOLMaster into a corrected corneal power, which is then input into the regular Haigis formula. The combination of the correction curve and the regular Haigis formula has been given the name Haigis-L, which is implemented in the IOLMaster software from Version 4 onward. An advantage of this formula is that it does not require any historic patient data, relying fully on currently available measurements. Biometry and keratometry are performed for a postrefractive surgery patient just as for a so-called normal cataract patient; the only difference lies in the selection of the formula for IOL calculation: for the refractive patient, the Haigis-L is chosen, and for the so-called normal patient, the regular Haigis or any of the other popular IOL formulas is selected. In 2008, our group published the first results of 187 cataract procedures after refractive laser surgery for the correction of myopia, performed by 57 surgeons from seven countries using this formula. 4 In the meantime, we have collected results for 91 more eyes, giving a total of 278 eyes (222 previously myopic and 56 hyperopic). The myopic eyes were supplied by 64 surgeons with 35 different IOL types and the hyperopic eyes by 15 surgeons with 13 different IOL types. For all cases, the IOLMaster was used for biometry (axial length and anterior chamber depth [ACD]) and keratometry. IOL power was calculated with the Haigis-L formula, in most cases prospectively. By comparison with the truly achieved stable postoperative refractions at distance BCVA, the following mean arithmetical prediction errors were derived: ±0.71 D for myopic eyes and ±0.77 D for hyperopic; the respective medians of the absolute prediction errors were 0.37 and 0.40 D. Correct refraction predictions within ±2.00 D, ±1.00 D, and ± 0.50 D were obtained in 98.6%, 82.9%, and 59.9% of the myopic and 96.4%, 82.1%, and 58.9% of the hyperopic eyes, respectively. These results compare favorably with normal eyes, although the error margins in predicted refraction are somewhat higher after refractive surgery. 34 Cataract & Refractive Surgery Today Europe may 2012

2 Wolfgang Haigis, MS, PhD, is a Professor in the Department of Ophthalmology, University of Wuerzburg, Germany. Professor Haigis states that he is a consultant to Carl Zeiss Meditec. He may be reached at tel: ; fax: ; [email protected]. 1. Haigis W. Intraocular lens calculation after refractive surgery. European Ophthalmic Review. 2012;6(1): Holladay JT. IOL calculations following RK. Refract Corneal Surg. 1989;5(3): Hoffer KJ. Intraocular lens power calculation for eyes after refractive keratotomy. J Refract Surg. 1995;11: Haigis W. IOL calculation after refractive surgery for myopia: the Haigis-L formula. J Cataract Refract Surg. 2008;34(10): Hoffer Q Theoretical Vergence Formula By Kenneth J. Hoffer, MD The year 1974 brought many firsts for me: I implanted my first IOL; I began organizing my first scientific meeting for the American Intra-Ocular Implant Society, which eventually became the American Society of Cataract and Refractive Surgery (ASCRS); I began working on a scientific peerreviewed journal for the society (Journal of Cataract and Refractive Surgery); I performed the first A-scan ultrasound axial length measurement for IOL power calculation in the United States; and, as a result of the latter, I wrote my first IOL power calculation formula. 1,2 The original Hoffer formula built upon Professor M.C. Colenbrander s formula. What made my variation unique from his and other existing formulas at that time, however, was that the desired postoperative refractive error could be added into the formula so the formula could be used to calculate the postoperative refractive error from any given IOL power. Also, the unit could be entered in diopters and AL and ACD could be entered in millimeters rather than meters. Eight years later, in 1982, I did a study that showed that the ACD and AL of the eye were directly proportional. I then updated my formula to calculate the ACD based on the AL (ACD = 2.92 x AL ). Jack T. Holladay, MD, introduced his Holladay 1 formula in 1988 using another component to IOL power calculations, when, in addition to AL, he began using corneal power (K) to calculate the position of the IOL using the Fyodorov corneal height formula. 2 At his instigation, I spent months and months trying to improve my formula to also include K. The result is a long, complicated formula that incorporates the factor of the tangent of K as well as the AL to generate an ELP; this is the Hoffer Q formula. In short, the Hoffer Q formula is the same as the 1974 Hoffer formula but using this additional Q formula to first calculate the ELP. PROGRAMMING THE FORMULA: PEARLS AND WARNINGS I am the first to admit that the Hoffer Q is a complicated formula, with certain factors that make it hard to program. For instance, the AL used in the Q formula does have a maximum value but obviously it is not limited in the vergence formula. The Hoffer Q is notoriously the worst formula to program by yourself; almost everyone who has programmed it based on the original publication in 1993 has gotten it wrong. 3 It is crucial to let me check the formula programming to ensure that is has been programmed properly. The best tip that I can give these practitioners is to use the Hoffer Q formula in the 1993 erratum rather than the original article, 3 because the journal had left out a minus sign and a parenthesis in the original article. I wrote another erratum in 2007, 3 listing common errors that practitioners make when programming the formula. This list is typically helpful for solving the majority of problems for most practitioners. I would also warn practitioners to use the formula in a licensed instrument, such as an ultrasound device licensed to use the formula, the IOLMaster, or the Lenstar (Haag-Streit). Using the Hoffer Q in a licensed machine means that I have had access to the equipment and have run the formula through 500 eyes to ensure that it is programmed correctly and licensed properly. My original study indicated that the Hoffer Q was comparable to the Holladay 1 formula in the normal range of eyes ( mm) but was less reliable in longer eyes (more than 24.5 mm.) It also indicated that it was more accurate in shorter eyes (less than 22.0 mm). I later proved this fact statistically (P<.05) in a study of 843 eyes shorter than 22.0 mm supplied to me by James P. Gills, MD (unpublished data). A recent study by Aristodemou et al, from the United Kingdom, on 8,108 eyes using the IOLMaster has statistically proven that this accuracy of the Hoffer Q in short eyes is real. 4 As far as postrefractive surgery eyes are concerned, the above obviously leads one to refrain form using the Hoffer Q formula in long eyes that have had myopic LASIK or PRK but definitely use it in eyes that have had hyperopic corneal refractive surgery. I am currently working with H. John Shammas, MD, on the Hoffer*Shammas formula, but that is a work in progress. Kenneth J. Hoffer, MD, is Clinical Professor of Ophthalmology at the University of California, Los Angeles, and practices at the St. Mary s Eye Center, Santa Monica, California. Dr. Hoffer may be reached at tel: ; [email protected]. may 2012 Cataract & Refractive Surgery Today Europe 35

3 1. Hoffer KJ. Mathematics and computers in intraocular lens calculation. Am Intra-Ocular Implant Soc J. 1975;1(1): Holladay JT, Prager TC, Chandler TY, et al. A three-part system for refining intraocular lens power calculations. J Cataract Refract Surg. 1988;14(1): Hoffer KJ. The Hoffer Q formula: A comparison of theoretic and regression formulas. J Cataract Refract Surg. 1993;19: ; errata: 1994;20:677 and 2007;33(1): Aristodemou P, Knox Cartwright NE, Sparrow JM, Johnston RL. Formula choice: Hoffer Q, Holladay 1, or SRK/T and refractive outcomes in 8108 eyes after cataract surgery with biometry by partial coherence interferometry. J Cataract Refract Surg. 2011; 37: Holladay 1 and 2: Theoretical Vergence Formulas By Jack T. Holladay, MD The Holladay 1 is a theoretical vergence formula that predicts ELP using a two-variable predictor with AL and K. First published in 1988, 1 the Holladay 1 was the first twovariable predictor of ELP using a theoretical vergence formula, which has stood the test of time for the past 25 years. We began a second study in 1993, enlisting 35 surgeons from all over the world to provide data for 35 short (less than 21 mm), 35 long (greater than 26 mm), and 35 normal eyes that would be representative of 35,000 cataract cases, as it takes approximately 1,000 eyes to get 35 within the correct range. We analyzed 10 variables and found that seven of these related to the ELP: AL, K, horizontal corneal diameter (white-towhite), ACD, lens thickness, refraction, and age. We introduced this seven-variable predictor of ELP using the theoretical vergence formula in 1995 and named it the Holladay In the most recent Leaming Survey (2011), conducted by Richard J. Duffey, MD, and David V. Leaming, MD, 50% of all US cataract surgeons reported that they used either the Holladay 1 or 2 formula for IOL power calculation. When all seven of the variables are entered into the Holladay 2, it is accurate in eyes from 15 to 35 mm in length. Other authors of formulas are beginning to use more of the seven variables we have used since 1995 (as many as five thus far, by Thomas Olsen, MD, PhD); however, the Holladay 2 remains the most comprehensive. Since 1995, more than 20 articles have found the Holladay 2 formula to be the most accurate or the second-most accurate formula for IOL power calculation Most authors usually find their own formulas to be the best on the data sets and, since the Holladay 2 was used to determine the formula, we are very happy to usually be No. 2. Jack T. Holladay, MD, is a Clinical Professor of Ophthalmology at Baylor College of Medicine in Houston. Dr. Holladay states that he is a consultant to Abbott Medical Optics Inc., AcuFocus, Oculus Optikgeräte GmbH, WaveTec, and Carl Zeiss Meditec. He may be reached at fax: ; [email protected]. 1. Holladay JT, Prager TC, Chandler TY, et al. A three-part system for refining intraocular lens power calculations. J Cataract Refract Surg. 1988;14(1): Holladay JT. Accuracy of Scheimpflug Holladay equivalent keratometry readings after corneal refractive surgery. J Cat Ref Surg. 2010;36: Trivedi RH, Wilson ME, Reardon W. Accuracy of the Holladay 2 intraocular lens formula for pediatric eyes in the absence of preoperative refraction. J Cataract Refract Surg. 2011;37(7): Ghanem AA, El-Sayed HM. Accuracy of intraocular lens power calculation in high myopia. Oman J Ophthalmol. 2010;3(3): Bang S, Edell E, Yu Q, Pratzer K, Stark W. Accuracy of intraocular lens calculations using the IOLMaster in eyes with long axial length and a comparison of various formulas. Ophthalmology. 2011;118(3): Holladay JT, Hill WE, Steinmueller A. Corneal power measurements using Scheimpflug imaging in eyes with prior corneal refractive surgery. J Refract Surg. 2009;25: Terzi E, Wang L, Kohnen T. Accuracy of modern intraocular lens power calculation formulas in refractive lens exchange for high myopia and high hyperopia. J Cataract Refract Surg. 2009;35(7): Haigis W. IOL calculation for high ametropia. Ophthalmologe. 2008;105(11): Lüchtenberg M, Kuhli-Hattenbach C, Fronius M, et al. Predictability of intraocular lens calculation using the Holladay II formula after in-the-bag or optic captured posterior chamber intraocular lens implantation in paediatric cataracts. Ophthalmologica. 2008;222(5): Hu BJ, Zhao SZ, Tseng P. Intraocular lens power calculation in cataract phacoemulsification after refractive surgery. Zhonghua Yan Ke Za Zhi. 2006;42(10): Narváez J, Zimmerman G, Stulting RD, Chang DH. Accuracy of intraocular lens power prediction using the Hoffer Q, Holladay 1, Holladay 2, and SRK/T formulas. J Cataract Refract Surg. 2006;32(12): Chan CC, Hodge C, Lawless M. Calculation of intraocular lens power after corneal refractive surgery. Clin Experiment Ophthalmol. 2006;34(7): Leccisotti A. Refractive lens exchange in keratoconus. J Cataract Refract Surg. 2006;32(5): Wang L, Booth MA, Koch DD. Comparison of intraocular lens power calculation methods in eyes that have undergone laser-assisted in-situ keratomileusis. Trans Am Ophthalmol Soc. 2004;102:189-96; discussion Wang L, Booth MA, Koch DD. Comparison of intraocular lens power calculation methods in eyes that have undergone LASIK. Ophthalmology. 2004;111(10): Packer M, Brown LK, Hoffman RS, Fine IH. Intraocular lens power calculation after incisional and thermal keratorefractive surgery. J Cataract Refract Surg. 2004;30(7): Preetha R, Goel P, Patel N, et al. Clear lens extraction with intraocular lens implantation for hyperopia. J Cataract Refract Surg. 2003;29(5): Gimbel HV, Sun R. Accuracy and predictability of intraocular lens power calculation after laser in situ keratomileusis. J Cataract Refract Surg. 2001;27(4): Seitz B, Langenbucher A. Intraocular lens calculations status after corneal refractive surgery. Curr Opin Ophthalmol. 2000;11(1): Kolahdouz-Isfahani AH, Rostamian K, Wallace D, Salz JJ. Clear lens extraction with intraocular lens implantation for hyperopia. J Refract Surg. 1999;15(3): Erratum in: J Refract Surg. 1999;15(6):620. Olsen Formula By Thomas Olsen, MD, PhD The calculation of IOL power in an eye that has undergone corneal refractive surgery is not a straightforward task. However, if you understand why the calculation may go wrong, you will have a fair chance of getting a good result using modern technology. It is important to understand that the calculation errors of post-lasik eyes are the sum of the traditional errors plus the errors associated with the abnormal corneal shape. The post-lasik eye exposes some of the weaknesses of the traditional IOL power calculation formulas. ERRORS OF TRADITIONAL FORMULAS Many of the old thin-lens IOL power calculation formulas, such as the Binkhorst, Hoffer Q, Holladay 1, and SRK/T use only the K reading and the AL as input. 1 When these formulas are used in post-lasik cases, two problems occur. 36 Cataract & Refractive Surgery Today Europe may 2012

4 Figure 1. The Fyodorov concept predicts the IOL position as a function of the corneal height (H), which is calculated from the corneal curvature and diameter. This model is used by the SRK/T formula and the Holladay formula (surgeon s factor [SF] is calculated as an addition to H). Figure 2. Distribution of the Gullstrand ratio in normal and post-lasik populations, as measured by Pentacam. Figure 3. Calculated change of the Gullstrand ratio as a function of the amount of excimer laser myopic ablation on a standard cornea. This figure also includes a regression equation stating the average change per diopter ablation. Figure 4. The difference between conventional K reading of the anterior surface and the true corneal power as a function of the Gullstrand ratio. Problem No. 1. The flatness of the K reading makes the formula believe the ELP is more anterior than it really is. With a shallow ELP, the formula will predict a low IOL power, causing a hyperopic surprise. Figure 1 explains Fyodorov s concept of the corneal height, which is the ELP principle of the SRK/T and the Holladay 1 formulas. Problem No. 2. A simple K reading measures only the curvature of the anterior surface of the cornea. However, most keratometers calculate the power according to the formula K = ( )/r, where r is the anterior radius in meters and is the fictitious refractive index of the cornea, as if the cornea were a thin lens. Therefore, in order for the anterior curvature measurement to be translated into the true power of the cornea, the following must be calculated: the curvature of the posterior surface, the corneal thickness, and the true refractive index of the cornea (1.376). In normal corneas, it is reasonable to assume that there is a constant ratio (called the Gullstrand ratio from the Gullstrand exact schematic eye) between the anterior and posterior curvatures. For the post-lasik cornea, however, the Gullstrand ratio is reduced, and the keratometerreported K reading will overestimate the true corneal power. Again, the formula will think the IOL power should be reduced, and the patient ends up with a hyperopic error. Modern Scheimpflug imaging and other tomography techniques provide more insight into the variation of the Gullstrand ratio in normal and post-lasik eyes. Figure 2 shows the results of Pentacam (Oculus Optikgeräte GmbH) measurement of the anterior and posterior corneal curvatures, giving the distribution of the Gullstrand ratio in a normal population and in a post-lasik population (average ablation, D). The reduction of the Gullstrand ratio is dependent on the amount of laser ablation (Figures 3 and 4). For example, if the Gullstrand ratio is 0.7 (ie, as a 38 Cataract & Refractive Surgery Today Europe may 2012

5 Figure 5. The prediction error with the SRK/T formula divided into two sources of error: K reading error and ELP error (postoperative ACD) as a function of the amount of laser ablation. Figure 6. Power distribution tool of the Pentacam. Figure 7. Fourier transformation of the central area, showing the spherical component. Figure 8. IOL power prediction error in 24 post-lasik cases plotted against the Gullstrand ratio. result of a 7.00 D ablation; Figure 3), the difference between the true corneal power and the K reading is approximately 2.00 D. However, for the normal cornea (Gullstrand ratio, 0.83), the difference is not nil. This is because the conventional K reading carries an inborn overestimation of the corneal power of approximately 1.00 D. The effect of the two sources of error on IOL power prediction with the SRK/T formula is shown in Figure 5. The K reading error and the ELP error are the same magnitude, and both tend to give a hyperopic error. The total prediction error is about one-third the amount of the excimer laser ablation if not corrected for. MY PREFERRED METHOD If available, pre-lasik K readings and amount of laser correction should be recorded. The historic method is not regarded as reliable, and therefore we use these data only to check whether our measurements are consistent. As with any other case, the patient should have optical biometry; I prefer the Lenstar LS900 biometer because this instrument measures all intraocular distances (corneal thickness, ACD, lens thickness, and AL) with the accuracy of laser biometry. Additionally, the pupil diameter is also measured. Next, the patient is examined with the Pentacam to determine the anterior and posterior curvatures of the cornea. I like to inspect the readings of the central cornea to check what the effective central reading might be. Useful tools of the Pentacam are its power distribution (Figure 6) and Fourier transformation (Figure 7) functions. These tools allow the surgeon to extract the effective radius in the pupillary area of the cornea. may 2012 Cataract & Refractive Surgery Today Europe 39

6 Figure 9. Pentacam data of front and back surface of the cornea transformed into a polygonal shape and imported by the Zemax software. The individual measurements can be found as points in a meshwork of miniature triangles, suitable for exact ray tracing. Ray tracing is performed directly on the raw physical shape without further model fitting. Figure 10. The optical system of a pseudophakic eye imported into Zemax software, in this case to solve for the optimal optical properties of the IOL giving the best image at the retinal plane. Insert shows the simulated quality of a Snellen letter projected on the retina. COMMENT Difficulties with reading the effective central part of the cornea add error to any formula. Keratometers usually measure the cornea in a noncentral ring of about 3 mm (about 2.5 mm with the IOLMaster). This is not adequate for a cornea with central flattening, and, in fact, all keratometers and topographers are blind to the central, most significant area of the cornea. Again, the potential error on the IOL power calculation is hyperopic. When information on the effective central anterior curvature of the cornea and the posterior curvature are available, we enter these values directly in the PhacoOptics software (PhacoOptics.com) using the Olsen formula for IOL power calculation. 2 The advantage of the Olsen formula is that equivalent K readings are not needed, as the program accepts direct input of front and back corneal curvature. Moreover, the Olsen formula uses an improved algorithm for the prediction of the IOL position, making it possible to base the ELP on the anterior segment anatomy only (ie, preoperative ACD and lens thickness) and avoiding troublesome K reading dependence (eyetube.net/?v=fuhal). In 24 eyes of 19 post-lasik patients for which the Olsen formula was used to calculate IOL power, we found a mean refractive prediction error of 0.41 ±0.68 D (range, to 1.63 D; Figure 8). There was no correlation with the Gullstrand ratio. The one patient with the highest error (1.63 D) was later reexamined and found to have a central cornea that was flatter than was measured at the preoperative visit, possibly caused by wearing a contact lens a few days before. The overall prediction accuracy is not as accurate as in normal eyes (and will never be), but we think the results are encouraging for our approach to be a feasible one. NEW DEVELOPMENTS: RAY TRACING As described above, much of the inaccuracy of IOL power calculations in post-lasik eyes is due to the problem of getting reliable information on the effective refractive power of the cornea. To this end, various models are often used to fit the corneal measurement to certain well-defined shapes, such as ellipsoids, Zernike polynomials, and Fourier transformations. In physical optics, ray tracing is widely used and recognized as the most effective tool in optical design. The eye is an optical device, so why isn t ray tracing the method of choice in our hands? The answer, perhaps, is because this technology is still evolving. We have recently begun a study to import the Pentacam raw height data into the Zemax software (Radiant Zemax, LLC) for optical engineering. 3 To import the data, we had to transform the matrix array of individual measurement points into a polygonal (Continued on page 65) watch it now on eyetube.net Using your smartphone, photograph the QR codes to watch the videos on Eyetube.net. If you do not have a QR reader on your phone, you can download one at eyetube.net/?v=fuhal 40 Cataract & Refractive Surgery Today Europe may 2012

7 A combination of linear regression method with a theoretical eye model. By Laura Straub, Editor-in-Chief SRK/T Formula: A Review Since 1975, IOL power has been calculated using accurate measurement of an eye s corneal power and axial length (AL). Prior to that, the power of the IOL was calculated using clinical history alone in other words, the preoperative refractive error prior to cataract development. The earliest IOL power calculation formulas, in the late 1970s and early 1980s, were either theoretical or regression formulas. Regression formulas topped surgeons preferences, and one of the most successful was the SRK formula devised by Donald R. Sanders, PhD, MD; John A. Retzlaff, MD; and Manus C. Kraff, MD. 1,2 The SRK formula uses the following equation to calculate IOL power: P = A BL - CK, where P is the implant power for emmetropia; L is the axial length (mm); K is the average keratometry (D); and A, B, and C are constants. The values of B and C are 2.5 and 0.9, respectively, and the value of A varies with the IOL design and the manufacturer. With this information, the formula can be written as follows: P = A 2.5L - 0.9K. Over the years, surgeons discovered that the SRK formula is best used in eyes with average AL, between and mm; a subsequent formula, the SRK II, was developed for use in long and short eyes. 3 In this formula, a correction factor was added to increase the lens power in short eyes and decrease it in long eyes: P = A1 0.9K -2.5L. For eyes with AL of less than mm, a numerical value of 3.00 is added to the A constant; a numerical value of 2.00 is added if the AL measures between and 20.99, a numerical value of 1.00 if the measurement is between and 21.99, and if the AL is greater than mm. Even more customized formulas are required today to calculate anterior chamber depth (ACD) based on AL and corneal curvature. The SRK/T (T for theoretical) is one such formula, representing a combination of linear regression method with a theoretical eye model. 4 Based on the nonlinear terms of the theoretical formulas, the SRK/T also incorporates empirical regression methodology for optimization, resulting in greater accuracy. The SRK/T and other third-generation formulas work best for near-schematic eye measurements; specifically, the SRK/T is best for eyes longer than mm. With this generation, which used an iterative process on five data sets consisting of 1,677 procedures, the SRK/T formula optimizes the prediction of postoperative ACD, retinal thickness AL correction, and corneal refractive index. It can be calculated using the same A constants used with the original SRK formula or with ACD estimates. 4 This calculation, however, does not account for effective lens position. 1. Sanders D, Retzlaff J, Kraff M, et al. Comparison of the accuracy of the Binkhorst, Colenbrander, and SRK implant power prediction formulas. J Am Intraocul Implant Soc. 1981;7(4): Sanders DR, Retzlaff J, Kraff MC. Comparison of empirically derived and theoretical aphakic refraction formulas. Arch Ophthalmol. 1983;101(6): Dang MS, Raj PP. SRK II formula in the calculation of intraocular lens power. Br J Ophthalmol Retzlaff JA, Sanders DR, Kraff MC. Development of the SRK/T intraocular lens implant power calculation formula. J Cataract Refract Surg The BESSt and BMR-BHR Formulas These formulas are useful for eyes that have previously undergone myopic or hyperopic laser treatments. By Edmondo Borasio, MD, MedCBQ Ophth, FEBO Using standard keratometry and raw data taken from corneal topography to calculate refractive corneal power in postrefractive surgery eyes can result in an inaccurate representation of the true corneal power. In these cases, instead of using a pseudophakic IOL power calculation that incorporates preoperative data, which can result in refractive surprises, I prefer to use direct corneal measurements. I use two approaches to calculate IOL power following laser refractive surgery, the first of which, the Borasio Edmondo Smith and Stevens formulas (BESSt and BESSt 2), is based on direct anterior and posterior corneal surface measurements and requires the Pentacam (Oculus Optikgeräte GmbH). 1 The second approach, the more recently developed Borasio Myopic Regression and Borasio Hyperopic Regression (BMR-BHR) formula, requires direct measurements from the IOLMaster (Carl Zeiss Meditec). These formulas can be used for eyes that have previously undergone myopic or hyperopic excimer laser treatments, even if there is a lack of prerefractive surgery information. 42 Cataract & Refractive Surgery Today Europe may 2012

8 BESSt AND BESSt 2 Based on direct anterior and posterior corneal curvature and corneal thickness measurements using the Pentacam and a modified Gaussian optics formula, the BESSt algorithm estimates corneal power in eyes after laser refractive surgery for myopia or hyperopia. It is not possible to use values obtained from the Gaussian optics formula in most current IOL power formulas because they are calibrated using a standard keratometric index of , which does not take true posterior corneal curvature into account. This can therefore yield inaccurate results, especially in postrefractive surgery eyes where the relationship between the anterior and posterior corneal radii is no longer constant. BESSt starts from the true net corneal power as calculated with the Gaussian optics formula, but then it makes crucial adjustments based on the actual measured postoperative corneal radii and the altered anterior/posterior radius relationship. We have found that the BESSt 2, a second iteration of the formula, results in greater prediction accuracy and less risk of refractive surprise after hyperopic treatments (unpublished data). BESSt 2 incorporates the following improvements compared with its predecessor: (1) automatic prediction of the preoperative anterior corneal radius from postoperative posterior corneal radius measurement, thus allowing automatic application of Aramberri s double-k adjustment for a more accurate prediction of the estimated IOL position, (2) two separate algorithms based on the results of regression analyses, one for myopic and one for hyperopic treatments, (3) automatic application of the BESSt 2-derived corneal power to a modified third-generation formula for the purpose of IOL power calculation, and (4) an error-limitation algorithm to prevent serious errors in eyes with extreme axial lengths. BMR-BHR The latest formulas I have developed for postrefractive surgery eyes, the BMR and BHR, require the use of the IOLMaster to measure K values and axial length. 2-4 From the measured postrefractive surgery K value, a new corneal power value is obtained by using one of these regression formulas. The resulting corneal power values are then automatically entered into the SRK/T formula, yielding a suggested IOL power. The BMR-BHR formulas are based on linear, logarithmic, and polynomial regression analyses and give similar results in most cases, with no greater than 0.25 D difference between the analyses with the exception of eyes with very steep or very flat corneas, where differences can be more substantial. Further studies are needed to determine which formula is the most accurate, but I tend to use linear regression. Polynomial regression has a smaller error in the majority of cases, but it can also have more serious outliers than linear regression; logarithmic regression lies in between the other two. It is best to use polynomial regression only when the suggested IOL power value is neither too low nor too high. BMR-BHR is currently available only as part of Eye Pro 2012 for the iphone/ipad. A desktop version will soon be available as an upgrade to the BESSt 2 IOL Power Calculator. CONSIDERATIONS AND RESULTS The same considerations apply to the BESSt, BESSt 2, and BMR-BHR formulas; they should not be used in the presence of significant corneal haze or scarring or after incisional refractive surgery such as radial keratotomy. Additionally, these formulas should be used with caution in eyes that have undergone astigmatic keratotomy; in eyes that have previously undergone myopic or hyperopic treatments for severe refractive errors; or in eyes that were operated on a long time ago using small optical zones. Other considerations include the following: The BMR-BHR requires K values specifically measured by the IOLMaster; I recommended comparing BESSt 2 with BMR- BHR. If the BESSt 2 formula suggests a very low (or very high) IOL power, I either use the BMR-BHR formula instead or the average of the two. It is always advisable to compare with other methods before proceeding with surgery. Whenever in the doubt, opt for a stronger IOL to target myopia; Be suspicious of very low or very high IOL powers resulting from BMR-BHR or BESSt in eyes with very steep or very flat corneas. These cases are at the extreme edges of any regression analysis, and the risk of a refractive surprise is high; and The BESSt 2 and the Eye Pro have not been approved by the US Food and Drug Administration (FDA) or received the Conformiteé Europeénne (CE) Mark. I recently conducted a study in 62 eyes, of which 38 received a myopic treatment and 24 a hyperopic, to compare the accuracy of the BESSt, BESSt 2, and BMR- BHR formulas. In the myopic group, BESSt and BESSt 2 performed similarly (mean error, ±0.78 D and ±0.81 D, respectively; P>.05), but in the hyperopic group BESSt 2 performed statistically significantly better (-1.10 ±0.90 D and 0.02 ±1.00 D, respectively; P<.05). The proportion of eyes within ±0.50 D of the intended target changed negligibly (from 37% to 38%) in the myopic group but improved significantly (from 13% to 38%) in the hyperopic group. The proportion of eyes within ±1.00 D of the target changed from 73% to 76% in the myopic may 2012 Cataract & Refractive Surgery Today Europe 43

9 Figure 1. Screenshots taken from Eye Pro 2012: (From left to right) BMR-BHR for IOLMaster, mobile version of BESSt 2 myopia, double-angle polar plot showing the average surgically induced astigmatism in a group of eyes, standard biometry on the go, and IOL power matrix. group and from 38% to 75% in the hyperopic group. Comparing the results with BESSt 2 to those with BMR and BHR, in the myopic group, the mean error was ±0.81 D with BESSt 2 and 0.00 ±0.75 D with BMR (P>.05). In the hyperopic group, the mean error was 0.02 ±1.00 D for BESSt 2 and 0.01 ±0.75 D for BHR (P>.05). Although these differences were not statistically significant, 31% more eyes were ±0.50 D or less from the target refraction with BMR compared with BESSt 1 and 30% more compared with BESSt 2. Similarly, with BHR 50% more eyes were ±0.50 D or less from the target compared with BESSt 1 and 13% more compared with BESSt 2. We believe this represents an improvement. PC VERSION FOR THE PENTACAM The BESSt 2 IOL Power Calculator (EB Eye Ltd, UK; besstformula.com) is available as an optional software add-on for the Pentacam. The main advantage of this calculator is that it can be installed on the same computer as the Pentacam. Therefore, calculations can be done directly from the Pentacam program by clicking on the BESSt 2 button, which will export all the required data (anterior and posterior corneal curvature and central pachymetry) to the program for the calculations. The program also keeps a database of calculations for future reference and for recalculation. A standalone version for research purposes is also available and can be used on a laptop not physically connected to the Pentacam hardware. Another feature of the BESSt 2 IOL Power Calculator for PC is real-time IOL power plotting to show the behavior of different biometry formulas when parameters are modified for any given axial length. This allows immediate identification of potential biometry artifacts that affect any given formula. Examples include the SRK/T negative square root and cusp phenomena that occur for certain combinations of axial length and K values (most frequently for steep corneas). When not identified, these artifacts can lead to inaccurate IOL power calculations. The BESSt IOL Power Calculator also allows the practitioner to compare the results with the historical method with or without the double-k adjustment, and using refractions at the spectacle or at the corneal plane for eyes for which prerefractive surgery information is available. A video presentation on BESSt and BMR-BHR is available at eyetube.net/?v=fireb. MOBILE VERSION AND APP A mobile version of the program, Eye Pro 2012 (Figure 1), is more suited for quick calculations. It includes not only BESSt 2 and BMR-BHR algorithms but also many other functions such as standard biometry and surgically induced astigmatism calculations. Our smartphone application (app) is a suite of ophthalmic calculators that includes the following advanced functions: Standard biometry (SRK/T, Hoffer Q formulas); BESSt 1 combined with third-generation formulas with double-k adjustment for biometry after refractive surgery; Toric IOL calculator that also accounts for surgically induced astigmatism (SIA); SIA calculator for K values or refractions; SIA plotter for group analysis showing both the vector and the arithmetic means; Visual acuity converter between Snellen/decimal/ logmar notation; Refraction converter between corneal/spectacle plane; Astigmatism converter between cartesian/polar notation; and 44 Cataract & Refractive Surgery Today Europe may 2012

10 watch it now on eyetube.net Using your smartphone, photograph the QR codes to watch the videos on Eyetube.net. If you do not have a QR reader on your phone, you can download one at Direct Link eyetube.net/?v=fireb Optical formulas including thin lens equation, Gaussian optics formula, and calculations using customized keratometric refractive indexes. Eye Pro 2012 is available for the iphone and ioscompatible devices and can be downloaded directly from the Apple store. A free trial version, Eye Pro Lite, is available at the Apple store and shows all the functions available in the 2012 version. n Edmondo Borasio, MD, MedCBQ Ophth, FEBO, is a Corneal Specialist and Consultant Ophthalmic Surgeon at Moorfields Eye Hospital Dubai. Dr. Borasio states that he is owner of and shareholder in EB Eye, Ltd. He may be reached at [email protected]. 1. Borasio E, Stevens J, Smith GT. Estimation of true corneal power after keratorefractive surgery in eyes requiring cataract surgery: BESSt formula. J Cataract Refract Surg. 2006;32(12): Borasio E. BESSt and beyond: The Borasio regression. Paper presented at the: 6th IOL Power Club Meeting; September 2010; Venice, Italy. 3. Borasio E. IOL power calculation accuracy in post-myopic and hyperopic ablations using the Borasio Regression formula. Paper presented at: the American Society of Cataract and Refractive Surgery Annual Meeting; March 2011; San Diego. 4. Borasio E. Post-LASIK IOL power calculation with Pentacam without pre-refractive surgery information. Paper presented at: the World Ophthalmology Congress; June 2010; Berlin. Take-Home Message The Haigis-L relies fully on currently available ocular measurements. The Hoffer Q is the same as the standard Hoffer formula but using the additional Q formula (tangent of K and AL) to calculate ACD. The Holladay 2 uses seven variables that relate to effective lens position: AL, K, horizontal corneal diameter, ACD, lens thickness, refraction, and age. The Olsen formula does not require equivalent K readings, relying on actual front and back corneal curvature. The SRK/T is a combination of a linear regression method and a theoretical eye model.

11 (Continued from page 40) shape that could then be imported by Zemax. When the data are successfully transformed, it is possible to construct the cornea as a meshwork of miniature triangles, suitable for exact ray tracing (Figure 9). The fascinating thing about Zemax and other ray tracing software programs is that it is possible to compose and analyze the entire optical system and ask for optimal performance of any element. For example, how should the IOL be designed to fit the optical properties of the cornea (Figure 10)? For the post-lasik cornea, it might be possible to solve for the higher-order aberrations of the selected IOL needed to correct for the HOA of the cornea. We expect this technology to be further elaborated in the future. n Thomas Olsen, MD, PhD, is a Professor of Ophthalmology at the University Eye Clinic, Aarhus Hospital, in Denmark. Dr. Olsen states that he is a shareholder of IOL Innovations, manufacturer of the PhacoOptics program. He may be reached at tel: ; fax: ; tkolsen@ dadlnet.dk. 1. Olsen T. Calculation of intraocular lens power: a review. Acta Ophthalmol Scand. 2007;85(5): Olsen T. Prediction of the effective postoperative (intraocular lens) anterior chamber depth. J Cataract Refract Surg. 2006;32(3): Olsen T, Funding M. Ray tracing analysis of the IOL power in situ. J Cataract Refract Surg. 2012;38: Share Your Feedback Would you like to comment on an author s article? Do you have an article topic to suggest? Do you wish to tell us how valuable CRST Europe is to your practice? We would love to hear from you. Please us at [email protected] with any thoughts, feelings, or questions you have regarding this publication. may 2012 Cataract & Refractive Surgery Today Europe 65