RESEARCH PROJECT. Retina and Vitreous Service, Hadassah Ein Keren Hospital, Jerusalem-Israel

Transcription

1 RESEARCH PROJECT IOL CALCULATION FOR HIGHLY MYOPIC EYES, COMPARISON OF DIFFERENT PUBLISHED METHODS. HADASSAH EIN KEREN HOSPITAL, JERUSALEM, ISRAEL, 2014 AUTHOR: Carlos Idrobo MD, Retina and Vitreous Service, Hadassah Ein Keren Hospital, Jerusalem-Israel SCIENTIFIC DIRECTOR: Dr Edward Averbukh. Retina and Vitreous Service, Hadassah Ein Keren Hospital, Jerusalem-Israel STATISTIC DIRECTOR Dr. Clara López de Mesa. Scientific Research Director, Barraquer Institute of America, Bogotá - Colombia 1

2 RESUMEN: OBJETIVO Comparar la precisión de varios métodos propuestos para mejorar el càlculo del lente intraocular en pacientes altamente miopes (mayor a 25 mm). LUGAR: Hospital Hadassah Ein Keren, Jerusalém Israel MÉTODOS: Se realizó una búsqueda de todos los casos de cirugía de catarata en pacientes con longitudes axiles de 25 a 30 mm en los cuales se calculó el lente intraocular mediante biometría óptica (IOL Master) usando la fórmula SRK/T, estos pacientes fueron operados de facoemulsificación y colocación de lente intraocular IQ SN60WF. Se realizó un cálculo regresivo del poder del lente intraocular mediante las fórmulas : SRK/T con constante optimizada (119.0), SRK/T con 3 constantes personalizadas de acuerdo a la queratometría, fórmula T2, fórmula T2 con constante optimizada (119.0) y fórmula Holladay 1 con factor del cirujano optimizado (1,84). Estos resultados se compararon entre sí buscando los métodos más precisos RESULTADOS: Se obtuvieron 55 casos correspondientes a 38 pacientes en los que el método más preciso fue el de SRK/ T con constante optimizada de con un Error Mediano Absoluto (EMedA) de 0.275, seguido por SRK/T con la constante original (EMedA:0,3), SRK/T con 3 constantes personalizadas ( EMedA: 0.31) T2 (EMedA: 0.33), T2 con constante optimizada (EMedA:0.38) y finalmente Holladay 1 con Factor del Cirujano Optimizado (EMedA:0.388). CONCLUSIONES: Los resultados muestran que el cálculo del lente intraocular SN60WF para pacientes altamente miopes usando los métodos de SRK/T con una constante optimizada de 119.0, SRK/T con 3 constantes personalizadas según la queratometrìa y fórmula T2 es más preciso. Se requieren estudios en poblaciones más grandes para aclarar las tendencias del presente estudio 2

3 ABSTRACT PURPOSE: To Compare the accuracy of various published methods to improve the IOL calculation in highly myopic patients ( higher than 25 mm) PLACE: Hadassah Ein Keren Hospital, Jerusalém Israel METHODS: Cases with an axial lenght higher than 25 mm to 30 mm which underwent cataract surgery were collected from the database of the Hadassah Ein Keren Hospital, the cases received Phacoemulsification surgery with IOL implant SN60WF, the calculation of intraocular lens (IOL) power was done using optic biometry (IOL Master) and the SRK/T formula. After successful surgery and followup period of minimum 3 weeks, the cases were evaluated by optometry and then a back calculation of the IOL power was done using the SRK/T with optimized A constant of 119,0; SRK/T with 3 IOL personalized constants according to the keratometry, T2 formula, T2 formula with an optimized A constant of 119.0, and Holladay 1 with an optimized surgeon factor of 1.84, the results were compared looking for the more accurate and for concordance between the methods RESULTS: 55 cases (eyes) were obtained, from 38 patients, the most accurate methods according to the median absolute error (MedAE) was SRK/T with an optimized A constant of (MedAE: 0.275), followed by SRK/T with the original constant (MedAE: 0.3), SRK/T with 3 personalized constants (MedAE0.31) and T2 formula (MedAE: 0.33), finally the Holladay 1 formula with Optimized Surgeon Factor (MedAE: 0.388) CONCLUSIONS: The results show that the IOL calculation for the SN60WF IOL in highly myopic eyes with the SRK/T formula using an optmized constant of 119.0, the SRK/T formula with 3 personalized A constants according to the keratometry values and the T2 formula show accuracy and concordance and can be used in these cases, A higher amount of cases is necessary to improve the tendency shown in the present sample. 3

4 INTRODUCTION Myopia can be defined as a refractive error in which parallel rays of light are brought to focus in front of the retina in a resting eye 1. High myopia, on the other hand, is defined as a spherical refractive power of 5 diopters or higher 2. The etiology of this condition is not well understood and factors like near sight activities performed since an early age and scant outdoor activity have been considered, genetic loci have been identified and approved by the Human Genome Organization Gene Nomenclature Committee, and called MYP 1 to MYP 14 in the chromosomes X, 1, 2-4,7,8,11,17,18,22, most of them related to high, early onset myopia 2 The worldwide prevalence of myopia ranges from 17 to 95% 3 A report regarding myopia in the United States, registered a prevalence of 33,1%,, most of these cases corresponded to young and white females 4. In A nation-wide study of myopia performed in Israel in 312,149 subjects, 17 to 19 years old, it was found that a 16,27% of this population was myopic, with an increased prevalence in female subjects 5. Another big study performed in Israel with a population of teenagers and young adults from 16 to 22 years old from 1990 to 2002, determined that the prevalence of myopia has increased in the cited population, with a remarkable change in the group of highly myopic eyes, which started on 13,5% in 1990 and increased to 20,7% in 2002 for female, and in male from 11,6% in 1990 to 16,3% in In regard of this information it is understood that some populations like the Israeli, show a tendency to increase the prevalence of its myopic patients, therefore, the incidence of high myopia will also increase. Also, while these populations become older, the need for an accurate intraocular lens (IOL) calculation for cataract surgery in myopic patients will also increase. Myopic eyes differ in many ways from emmetropic eyes. A longer axial length, an increased diameter of the lens capsular bag and a deeper anterior chamber are 4

5 found 7, these features are responsible of a deeper position of the IOL in the bag, which also is related to an hyperopic surprise after IOL calculation 8. On the other hand, the IOL s positioning in the bag is also affected, the posterior capsule takes more time to make contact with the posterior IOL s surface 7. some concepts must be taken into account when calculating IOLs for myopic patients, which include: 1. The Axial length (AL) patients with a staphiloma are considered a problem when measuring with ultrasound, the optic biometry is able to overcome this pitfall because the measurements can be done respect to the fixation point of the patient. 8 In spite of this statement, Olsen and Thorwest 9 found that the preoperative AL was longer than the post-operative axial length by around 0,08 mm on average, and a proposed a model of the phakic eye with a slightly higher refractive index of 1,3616 was developed. Other authors describe transformation formulas to improve the AL measurement by the IOL master, examples are found in the studies by Preußner et al 10 and Li Wang et al 11 who found a reduction in the amount of eyes left hyperopic using methods of back calculation of AL in order to obtain a prediction error of 0. Another problem related with the AL is specific to the commonly used formula SRK/T, which requires a correction when measuring AL longer than 24,2. This was fixed by the original authors with a change in the step 2, introducing a corrected axial length (LCOR) according to the following calculation: If LCOR 24,2 then LCOR= -3, ,716 x 36,2 0,0237 x 36,2 In spite this correction, Sheard et al. documented that when the AL reaches a value of 36,2 mm, the LCOR reaches a maximum of 27,62 mm and, after this point, the LCOR decreases while the actual AL increases, this is an illogical behavior called the LCOR reversal, the cited author states that when the AL is greater than or equal to 36.2 mm, LCOR should be a constant (LCOR = mm). This calculation is part of the T2 formula 5

6 which also makes a correction in the corneal height, this will be reviewed later in the text The anterior chamber depth (ACD) is defined as the axial distance from the central front surface of the cornea to the central front surface of the crystalline lens, it plays an important role as a source of error in cases where the AL has been accurately measured, this is because the ACD is related to the effective lens position (ELP), which is the distance from the anterior surface of the cornea to the effective main plane of the IOL in the visual axis. The ACD and ELP are part of the calculation of the IOL constants used in the different formulas, for example, in order to calculate the A constant for the SRK/T formula, the ACD is necessary (A = [(ACD ) ]0.5663) the same thing happens with the Surgeon factor from Holladay s formula (SF = ACD 3,595). The conclusion is that the ELP is contained in the A constant 8. A higher value of an A constant is reflected by a longer ACD value, most of the time this combination will be observed in the presence of a long eye. Petermier et al. describe that a more accurate AL measurement could not improve the IOL calculation for highly myopic eyes, and instead of facing the issue by changing the AL like the previous description, these authors calculated individualized IOL constants based on the postoperative refractive results, separately for the positive-diopter and negative-diopter ranges within the framework of the User Group for Laser Interference Biometry project to optimize constants for optical biometry, the cited authors performed a study in which they optimized the IOL constants, the base of this procedure was the assumption that the main error in IOL calculation was the difficulty to measure the ELP properly, this because of, 1) the IOL lens calculated can be negative, positive or zero, a fact that changes the calculation patterns (most formulas are not designed to deal with negative 6

7 values). 2) The anatomy of the lens is also changed when there is a positive or negative lens, because the main plane of the lens moves, according to the power required. The optimization of constants allowed them to reach a refractive deviation of zero in positive and negative IOLs using the Haigis, Sanders Retzlaff Kraff/T (SRK/T), Holladay, Hoffer Q, and Sanders Retzlaff Kraff II (SRK II), although the intraocular lenses with a value of zero didn t perform that well in the sample. 13. Youngsub et al, demonstrated a median absolute error decrease from 0.29 D to 0.23 D using the SRK/T formula with personalized optimized constants, using the IQ intraocular lens, (P= 0.001). The conclusion of the study was that for a steep cornea, the calculated A-constant would be of a lower value, but for a flat cornea, a higher magnitude A-constant was necesary. The use of personalized A-constants based on the keratometic values showed improvement in the refractive outcomes Corneal height. A big study by Sheard et al. using eyes concluded that the SRK/T, has a non-physiological behavior when calculating IOL power in certain keratometric values, this means that with certain axial length and keratometric readings, the estimation of the corneal height value does not follow a normal curve, but has an unexpected peak, known as the corneal height cusp, after this point, the gradient reverses and all the curves show an almost linear relationship. The shape of the corneal height curves suggests that in the vicinity of the cusp, the SRK/T formula may overestimate the corneal height. The original SRK/T formula changes negative values of X, to 0, in order to prevent the formula from attempting to take the square root of a negative number, this is the solution to the ACD problem. In this region, the corneal height was equal to the corneal radius of curvature. 12 In order to deal with this pitfall,, the referred authors considered that a new corrected formula based on the SRK/T, this formula was published under 7

8 the name of T2 and has a reported 10% improved accuracy (with a lower IOL mean error than the calculations performed by the regular SRK/T). 12 The T2 formula overcomes the non-physiological behavior of the corneal height of the regular SRK/T formula correcting the steps 2 to 4 by a regression formula: H2= -10, ,32630 x L + 0,13533 x K. With this calculation, it is possible to avoid the peak in corneal height calculation which appears in a point when combining specific AL and Keratometric values, the ones of our interest would be the curve of 24 mm axial length which peak is found at around 50 diopters of mean keratometry, 26 mm, around 47 D and 28 mm around 46 D. 12 To the best of our knowledge, no publication has compared the described methods, therefore, an study using the SRK/T formula without A constant optimization, SRK/T with 1 optimized A constant (taken from the ULIB website), SRK/T with 3 optimized A constants personalized according to the keratometric values, T2 formula, T2 formula with 1 optimized A constant (taken from the ULIB website), and the Holladay 1 formula with an optimized Surgeon Factor (taken from the ULIB website) is proposed. 8

9 METHODS Study design: Observational analytical retrospective cohort Population: Highly myopic patients, defined as those having more than -5 D of spherical power lens correction, which underwent uneventful crystalline lens phacoemulsification and IOL insertion in the Hadassah Ophthalmology clinic from June 2012 until January 2014 in one of the surgeon s surgical practice (Dr EA). Institutional review board approval was obtained from The Hadassah Ein Keren Hospital, Jerusalem, Israel. All research and data collection followed the tenets of the Helsinki Agreement. Inclusion criteria: Highly myopic patients (AL longer than 25 mm), implant of IOL Acrisoft SN60WF acrylic, A constant 118.7, Visual acuity > 20/40 in the operated eye, after cataract surgery Exclusion criteria: Patients who were not measured by optical biometry, patients who suffer of any ophthalmological condition that could affect the accuracy of biometric measurements, (retinal detachment surgery, corneal scars), patients that have suffered of any ophthalmological condition that could affect their best corrected visual acuity apart from their cataract (choroidal neovascularization due to myopia or NVAMD, Diabetic Macular Edema, Optic Atrophy or Optic neuritis) appearing previous to the surgery or during the time the patients are being followed, myopic degeneration and glaucoma patients would be excluded only if their condition affects severely the visual acuity, traumatic cataract cases, previous ocular surgery (pe netrating keratoplasty), complicated surgery (e.g., anterior or posterior capsular tears), sulcus fixated lenses, IOL exchanges, postoperative complications, indwelling silicone oil history of any kind of refractive surgery in the case) Variables: The following information should be obtained from the clinical records to calculate the IOL according to the methods previously described: AL, measured with the IOL Master, K1, K2, measured with IOL Master or autorefractometer 9

10 keratometry, if IOL Master measurement was not available, best corrected Preoperative VA, measured with the ETDRS chart, converted to fraction, best corrected Postoperative VA. measured with the ETDRS chart, converted to fraction, lens A constant and other constants required according to the formulas used, post operative spherical power, post operative cylinder, post-operative spherical equivalent, IOL Prediction deviation from the target refraction in the postoperative. The refractive prediction error will be calculated according to the analysis published by J. Aramberri 15 : which includes the following steps: 1) The expected refraction with a certain IOL power was subtracted from the expected refraction from an IOL 1,0 Diopter higher or lower than the first one.2) 1 is divided by this value, resulting in the magnitude in IOL power that should produce 1.0 D of refractive change (IOL1DRx). 3) This value was multiplied by the refractive error (Rx) calculation and added to the implanted lens power. The result is the emmetropic power in the case. The IOL power required for emmetropia in the case is subtracted from the IOL power that would lead to the refraction target and this is divided by the IOL1DRx value, the result is the predicted refractive error that would be obtained with this method, finally, this is subtracted from the original refraction target in order to know the numerical error, and this value is converted to absolute values to obtain the absolute numerical error, this operation was repeated for the other methods included in the present study. The IOL power calculation methods included were: SRK/T with original constant, SRK/T with optimized constant (SRK/T O.C.), T2, T2 with optimized constant (T2 O.C.), SRK/T with 3 Optimized constants according to the K value (119,08 for K lower than 43,0 D; for K from 43,0 to 44.7 D and for a K higher than 44,7 D 14 ) and Holladay 1 with Optimized Surgeon Factor (Holladay 1), for each method the following values were obtained: IOL power, IOL power equivalence in the glasses plane using the formula, IOL deviation from target refraction, percentage of cases with an error within + 0,50 D, from +0,50 to +1,00 D, from +1,00 to +2,00 D and within an error to +2,00 D 10

11 The Optimized A constant for the 118,7 Alcon IOL, SN60WF is 119,0 according to the ULIB group with 5128 cases 16, The Holladay 1 Surgeon Factor (S.F) of 1.84 was used according to the ULIB website. Mean numerical and absolute error as well as median absolute error were compared between methods, employing the Lin s coefficient of Correlation and Concordance. Correlation between mean Keratometry and Absolute error (AE), as well as between AL and AE were measured with Pearson s coefficient. The analysis was done using Excel 2013, Graph Pad Prism 6,0, MedCalc and SPSS software 12.0 (SPSS Inc., Chicago,IL) 11

12 RESULTS Descriptive statistics Demographics: After using the inclusion and exclusion criteria, 38 patients were obtained, with a mean age of 68,47 years old (Standard Deviation(SD): 10,31, maximum value: 85 years old, minimum value: 43 years old), and a gender distribution of 55,2% female (21 patients) and 44,7% male (17 patients).from this group, a total of 55 eyes (cases) underwent Phaco + IOL procedure. Preoperative status: The visual acuity is presented as a fraction from the ETDRS chart.in the preoperative visit had a mean of 0,3565 (SD: 0,2303, min: 0,05, max: 0,9). The axial length had a mean of 26,84 mm, (SD: 1,128mm, min: 25,18mm, max: 30,08mm). The keratometries showed the following values: K1 had a mean value of 43,56 diopters (SD 1,532 D, min 39,94D, max 46,81 D) and K2 had a mean value of 44,5 diopters (SD 1,429 D, min 40,23D, max 47,6 D), the mean keratometry was 44,03 Diopters (SD: 1,441 D, min: 40,08D, max 47,2D). The refraction target of the studied group had a mean of -1,749 Diopters (SD: 1,218 D min: 5 D, max: 0,68 D), The extreme -5 D refraction target was the case of one patient who didn t want to be operated in his second eye since he had a history of uveitis under control. Preoperative remarks of the studied cases included: Previous uveitis, not active at the moment of the surgery in three cases, significant peripapilary atrophy in one case, pseudoexfoliation syndrome in two cases, convergence defect in one patient, mild macular pseudohole in one case, and atrophic retinal changes without macular involvement in two cases. One case with staphyloma was registered 12

13 Actual surgical IOL Calculations: The Intraocular Lens (IOL) power calculations were first performed using the SRK/T with original constants, for the actual surgeries in which the IOL for refraction target was implanted, the value which would lead the case to emmetropia was calculated according to the method described previously 15. These results are summarized in table number 1. The actual refraction of the patients was obtained and converted to spherical equivalent, and the expected target refraction with which the IOL was calculated, was subtracted from this spherical equivalent, this value was used to measure the prediction error whicha was called numerical error, the absolute values were used to obtain the mean absolute error. Then errors expressed in diopters were grouped according to their magnitudes. From the calculated series, using the SRK/T with the original constant of 118,7, the Mean numerical error (MNE) was 0,049±0,65 (Min -1,965 Max 1,450) and the Mean absolute error (MAE) was 0,4768±0,467 (Min 0 Max 1,965). 70,9% (39 cases) had a ± 0,50 D error, 10,9% (6) had an error ranging from ±0,50 to 1,00 D, 14,5% (8) had an error of ± 1,00 to ±1,50 D while a 3,6% (2) had an error of ± 1,50 to ±2,00 D. Postoperative evaluation The best corrected visual acuity of the cases included had a mean of 0,8347, Standard deviation of 0,1837, (Min 0,5 Max 1,25). The postoperative refractive status of the cases was evaluated, these results are resumed in table number 2.The studied cases underwent uneventful surgeries, without complications in the postoperative time lapse. 1. IOL Calculation with different methods. The T2 formula: The IOL power calculated using this formula for the desired refraction target and for emetropia are summarized in table number 3.The mean numerical error (MNE) using this formula was 0,044 D (SD:0,687 D min: -2,078D 13

14 max:1,40d). the Mean Absolute Error (MAE) was 0,503 Diopters (SD 0,465 D min: 0,010 D, max: 2,078 D). The percentage of cases falling within ± 0,50 Diopters was 65,45% (30), from ± 0,50 to ± 1,00 it was 20%(11), from ± 1,00 to ± 1,50 diopters it was 12,72% (7), from ± 1,50 to ± 2,00 diopters it was 0% (0) and an error bigger than ± 2 D it was 1,81%(1) T2 fórmula with Optimized constant In an attempt of improving the results, the T2 formula was used together with the Optimized contstant of 119,0 provided by the ULIB website. The IOL results of this method are shown in table number 4. The MNE with this formula was -0,109 Diopters (SD: 0,67 D, min:-2,174 D max 1,239 D), the MAE was 0,49 D (SD: 0,466 D,min 0,0066 D, max 2,174 D). The percentage of cases falling within ± 0,50 Diopters was 65,45% (36), from ± 0,50 to ± 1,00 it was 20%(11), from ± 1,00 to ± 1,50 diopters it was 10,9% (6), from ± 1,50 to ± 2,00 diopters it was 1,81% (1) and an error bigger than ± 2 D it was 1,81%(1) The SRK/T formula, with an optimized constant of 119,0 generated the IOL power for refraction target and emmetropia which appear in table 5. The MNE using this method was -0,081 D (SD: 0,65 D, min: -2,05 D, max: 1,304 D). the MAE was 0,456 Diopters (SD: 0,4711 D, min: 0,011 D, max: 2,06 D). The percentage of cases falling within ± 0,50 Diopters was 67,27 % (37), from ± 0,50 to ± 1,00 it was 18,18%(10), from ± 1,00 to ± 1,50 diopters it was 10,90% (6), from ± 1,50 to ± 2,00 diopters it was 1,82% (1) and an error bigger than ± 2 D it was 1,82%(1). Holladay 1 formula with an optimized surgeon factor (SF) of 1,84 provided an IOL power as shown in table number 6, for both target refraction and emmetropia. The MNE with this formula was -0,232 Diopters (SD: 0,65 D, min: -1,51D max 1,58D), the MAE was 0,514 (SD: 0,456 D min, 0,022 D, max 1,58 D). The percentage of cases falling within ± 0,50 Diopters was 63,63% (35), from ± 0,50 to ± 1,00 it was 16,36%(9), from ± 1,00 to ± 1,50 diopters it was 16,35% (9), 14

15 from ± 1,50 to ± 2,00 diopters it was 3,63% (2) and an error bigger than ± 2 D it was 0%(0) Finally, the last method used in comparison with the previously described ones is the SRK/T with 3 constants, the results of this method are resumed in table number 7. The Median Absolute Error (MedAE), was calculated for the all the methods and is presented in a comparative way in table number 8. Graph number 1 summarizes and compares de outcomes of the MNE of the 6 formulas used for calculation in the present series. While graph number 2 shows the behavior of the MAE. Correlative Analysis A) Concordance Correlation Coefficient of Lin In order to improve the analysis, a Concordance correlation coefficient of Lin was calculated between all the methods, these calculations are summarized in table number 9 for Absolute Error. The following methods showed concordance: T2, T2 calculated with Optimized Constant of 119,0 (T2 + OC), SRK/T with Optimized Constant (SRK/T OC) of 119,0 and SRK/T with 3 Optimized constants Graphics number 3-8 show the scatter diagrams of the Absolute Error from these correlations. The relationship between the keratometry and the absolute error was also analyzed, no correlation was found with any method in the present sample. Table number 10 summarizes the data. On the other hand, a grouped analysis in order to find keratometric values where the absolute prediction error could be higher was also performed, the results are shown in table 11 A and 11 B. 15

16 The absolute error - axial length relationship was also analyzed, no correlation was found with any method in the present sample. Table number 12 summarizes this information.also a grouped analysis was performed between different axial lengths and the median absolute error, this is shown in table number 13. The Absolute error did not show a Gaussian distribution using the D'Agostino & Pearson normality test. DISCUSION In the present study, the method which showed the lowest Median Absolute Error was the SRK/T formula with an optimized A constant of 119,0 for the SN60WF lens (median absolute error: 0,2753). The accuracy of this method might be related to the high amount of cases provided for the A constant database used in the ULIB website (more than 5300 cases) 16, and is consistent with previous evidence showing the benefits of this method 17. In regard gf the evidence of the not physiologic behavior of the SRK/T formula when some K values are reached, a group analysis based on the mean keratometry was performed, it showed that the median absolute error (MedAE) of the SRK/T formula with the Optimized A Constant of 119,0, increased with values 44,7 D as shown in table 11 A (Median error of 0,2981) and more specifically in the group from 44 to 46 D group (Median error of 0,27) as shown in table 11 B, this agrees with what was described by Youngsub et al, who found that the SRK/T had an increased error in the extremes of the keratometric values, and suggested the use of personalized constants for cases with keratometries lower than 43.0 D which would benefit from an A constant of , cases from 43.0 D to 44.7 D which would have better results with an A constant of and those with a K higher 44,7 D that would require a K of Using the 3 constants reduced the median error from 0,36 to 0,24 in the cited report 14 Therefore a calculation with the 3 constants described in cited article was tested, these results are shown in table N. 13, the median absolute error found was 0,31 D which in comparison with 16

17 the other methods used, was slightly higher than that of SRK/T with the optimized A constant of 119,0 and the SRK/T with a non optimized A constant of 118,7. This could result from the necessity of further optimization of the 3 A constants for each surgical center, also, multicenter reports following the same A constant optimization protocol may be necessary in order to obtain a database which could be applied to different places.. In spite of the median error being higher for the 3 A constant optimized method than that of the SRK/T with one optimized A constant in the present sample, it is possible to see that the median absolute error in the individual keratometric groups Is kept very low and similar to that of the 1 optimized constant SRK/T as seen in table number 11A The T2 formula avoids the not physiological peak in corneal height calculation which appears in a point when combining specific AL and Keratometric values, the ones of our interest would be the curve of 24 mm axial length and 47 diopters of mean keratometry, 26mm, with 46 D and 28 around 45,5 D 12. These combinations of AL and Keratometric values are not common, but the T2 formula is able to overcome this issue. The mean keratometry of the present study was 44,03 D and the mean axial length was 26,84 mm, this means that at the least the mean values of the present sample, are not yet inside the slope areas of the not physiological behavior cusps of the regular SRK/T, allowing the calculations made by the SRK/T to be accurate within the limits of this study. The mean absolute error found in the present article with the T2 formula without constant optimization is of 0,5039 with a Median Absolute error of 0,33. The Mean absolute error found in the original article of the T2 formula was 0,3064. Since the sample used for the original T2 study is big, around 5600 cases, it is clear that the distribution of the data will be Gaussian, and therefore closer to the median, so it is possible to state that the median absolute error in the present study is similar to the mean absolute error found by Sheard et al. 12 The same is true for the T2 formula used in conjunction with the Optimized constant, which Median absolute error is not far from the mentioned one (0,38). 17

18 A more detailed study comparing the absolute error and the keratometry showed that the best performance of the T2 formula in the present study was in the group of 42 to 44 D (MedAE:0,312), and the worse wa s in the group of 46 to 48 D (MedAE: 0,4928). The T2 with A constant optimization showed the best results in the 44 to 46 D (MedAE: 0,230), and the worse results in the 40 to 42 D (MedAE: 0,517). In this regard we could suggest that either an A constant personalization or a different optimized constant is necessary to further improve the results of the T2 formula. In any case, this formula has shown adequate correlation with the SRK/T formula with an optimized A constant, and therefore it can be used as good tool for IOL calculation in highly myopic cases. The Holladay 1 formula was also calculated using the ULIB optimized surgeon factor of 1,84, a median absolute error of 0,3883 was obtained, being this the higher between the methods compared in the present study, this fact could be explained by the already documented reduced accuracy of the Holladay 1 formula for IOL calculation in eyes with axial lengths longer than 26 mm 18. The Mean absolute error reported for this method in the present study of 0,5138 is similar to the mentioned study by Hoffer for very long eyes, where the error is 0, The Median Absolute error is of a higher magnitude than the reported by Li Wang, which had a value of 0,40 11, in which the IOL calculation was improved, optimizing the AL with a back calculation. According to these findings we understand that optimizing the Surgeon Factor is not enough to improve the accuracy of this formula, and that an AL based optimization is necessary in order to improve the results. All the methods used in this study were tested for concordance, using Lin s 19, 20 Concordance and Correlation coefficient taking the absolute error as the output comparison variable, the SRK/T with Optimized Constant was used as the gold standard because of its accuracy proved in several publications 8,16,17 18

19 The result of this analysis showed concordance between SRKT with optimized A constant, T2 formula, and T2 with optimized constant, according to this, the concordance between SRK/T with Optimized A Constant and the T2 formula was moderate (0,90), this was the same for the concordance between the SRK/T with Optimized Constant and T2 with Optimized A Constant (0,91). Also the SRK/T with 3 Optimized constants showed a moderate concordance with the T2 formula (0,91), and a substantial concordance with the SRK/T with optimized constant of 119,0 (0,96) and T2 with optimized constant of 119,0 (0,959). This shows that this method can also be used as a good tool for IOL calculation in highly myopic patients. The concordance between SRK/T with Optimized constant with the Holladay 1 formula with Optimized Surgeon Factor was poor (0,78 for the second). The concordance results are summarized in table 8 and graphics 3 8, showing that the three methods referred (SRK/T with Optimized A Constant of 119, SRK/T with 3 optimized A constants, T2, T2 with Optimized Constant) can be used obtaining good results in highly myopic eyes. In the present study the SRK/T with 1 A optimized constant still shows superiority respect to the other formulas. A correlation between the absolute error and the keratometric values was sought, but no method showed significant p values for the Pearson correlation coefficient, this information is summarized in table N. 9 The relationship between axial length values and the absolute error was also analyzed, finding no Pearson s correlation coefficient of statistical significance as shown in table N. 11, a grouped analysis was also done, in order to identify if a specific axial length showed higher median error, this information is summarized in table N. 12. The results from this last analysis are not conclusive since some of the groups have few cases. A comparison of the present study with other studies is provided in table

20 From the present study we can conclude that Myopic IOL calculation is still far from being as accurate as that for normal eyes, in any case several methods have been proposed to overcome this problem, being the SRK/T with an optimized constant, one of the most explored since the constant optimization process is relatively easy to obtain the more accurate IOL A constant, also several groups around the globe are providing thousands of cases with IOL constants optimized for commonly used IOLs, this is the case of the ULIB web site of Zeiss, which can become a very useful tool for those interested in improving their results when it comes to IOL calculation for myopic patients. Using the SRK/T formula with the correct optimized constant shows excellent results. The use of Holladay 1 formula for highly myopic eyes (AL longer than 26 mm) is not encouraged, since even with a Surgeon Factor constant optimization, the results are less accurate than those of the SRK/T. The T2 formula with or without an A constant optimization also provides very accurate results, although in the the present sample, the use of the optimized constant of 119,0 showed worse results than those with the regular 118,7 A constant, therefore more studies in order to obtain a better constant optimization for the T2 formula are encouraged. Advantages of the present study include a homogeneous sample, with eyes with high myopia, operated by the same surgeon and with the same IOL implanted, also the calculations were performed using exclusively the IOL Master optical biometry in a single center, also four documented methods are compared and the T2 formula is used for the first time in a study besides the original one. Pitfalls of the present study include a relatively small sample size. The A constant optimization is a useful method to improve the results of the SRK/T formula lowering the Median error, for the IQ IOL, the optimized A constant widely calculated is of 119,0, according to the ULIB website, and used in the present study, this approach proved to be accurate. 20

21 The authors would like to acknowledge Dr. Sheard for providing the necessary software for IOL calculation with the T2 formula as well as the Barraquer Institute of America research head, Clara Lopez de Mesa, who provided advice for the statistical analysis. 21

22 References 1. Seang-Mei Saw, Joanne Katz, et al Epidemiology of Myopia, Epidemiologic Reviews No2, 1996, pg Hornbeak Dana, Young Terri et al, Myopia genetics: a review of current research and emerging trends, Current Opinion in Ophthalmology, Vol. 20, September 2009, p Nangia V, Jonas JB et al, Refractive error in Central India: The Central India Eye and Medical Study, Ophthalmology, 2010; 117(4): Vitale S,Ellwein L, et al, Prevalence of refractive error in the United States, , Archives of Ophthalmology, 2008, 126, Rosner M, Belkin M, A nation-wide study of myopia prevalence in Israel. Findings in a population of 312,149 young adults, Metabolic Pediatric and Systemic Ophthalmology, 1991; 14(2), Yosefa Bar Dayan, Avi Levin, The Changing Prevalence of Myopia in Young Adults: A 13-Year Series of Population-Based Prevalence Surveys, Invest Ophthalmol Vis Sci. 2005;46: Yinying Zhao, Jin Li and associates, Capsular Adhesion to Intraocular Lens in Highly Myopic Eyes Evaluated In Vivo Using Ultralong-scan-depth Optical Coherence Tomography, American Journal of Ophthalmology 2013;155: Kenneth J. Hoffer, MD and asociates, IOL Power formulas & special circumstances, 2010, American Academy of Ophthalmology. 9. Olsen T, Thorwest M. Calibration of axial length measurements with the Zeiss IOLMaster. J Cataract Refract Surg 2005;31: ) 10. Preußner P-R, Olsen T, Hoffmann P, Findl O. Intraocular lens calculation accuracy limits in normal eyes. J Cataract Refract Surg 2008; 34: Li Wang, MD, PhD, Mariko Shirayama, Optimizing intraocular lens power calculations in eyes with axial lengths above 25.0 mm, J Cataract Refract Surg 2011; 37: ), 22

23 12. Sheard R, Smith G, et al, Improving the prediction accuracy of the SRK/T formula: The T2 formula, Journal of Cataract and Refractive Surgery 2010; 36: ). 13. Petermeier, K, Gekeler F, Intraocular lens power calculation and optimized constants for highly myopic eyes, J Cataract Refract Surg, : ) 14. Youngsub Eom, MD, Su-Yeon Kang, MD, Use of Corneal Power-Specific Constants to Improve the Accuracy of the SRK/T Formula Ophthalmology 2013;120: ) 15. Jaime Aramberri, MD Intraocular lens power calculation after corneal refractive surgery: Double-K method, J Cataract Refract Surg 2003; 29: Optimized IOL Constants for the ZEISS IOLMaster calculated from patient data, ULIB,User Group for Laser Interference Biometry, accessed the 23/4/ Olsen T, Corydon L, Gimbel H. Intraocular lens power calculation with an improved anterior chamber depth prediction algorithm, J Cataract Refract Surg May;21(3): Hoffer KJ. Clinical results using the Holladay 2 intraocular lens power formula. J Cataract Refract Surg. 2000;26(8): Lin LI. A concordance correlation coefficient to evaluate reproducibility. Biometrics. 1989; 45, McBride G.B, A Proposal for Strength of Agreement Criteria for Lin s Concordance Correlation Coefficient, NIWA Client Report: HAM , May 2005, NIWA Project: MOH 05201pp:5-6 23

24 Tables and graphics Table Number 1 IOL CALCULATION WITH SRK/T FORMULA SRK/T CALCULATION FOR TARGET REFRACTION SRK/T CALCULATION FOR EMMETROPIA MEAN 13,1 Diopters 10,31 Diopters S. DEVIATION 2,739 D 3,12 D MINIMUM 6 D 0,85 D MAXIMUM 18 D 16,5 D n= 55 cases (eyes) Source: Database of clinical records, Ophthalmology department, Hadassah Ein Keren Hospital, Jerusalem Israel. Table Number 2 POST OPERATIVE REFRACTIVE RESULTS SPHERE CYLINDER AXIS SPHERICAL EQUIVALENT MEAN -1,436 Diopters -0,7227 Diopters 80,38 degrees -1,798 Diopters S. DEVIATION 1,184 D 0,7693 D 62,29 degrees 1,325 D MINIMUM -4,25 D -2,5 D 0 degrees -4,75 D MAXIMUM 0,25 D 1,25 D 180 degrees 0,625 D n= 55 cases, Source: Database of clinical records, Ophthalmology department, Hadassah Ein Keren Hospital, Jerusalem Israel. Table Number 3: IOL POWER CALCULATION USING THE T2 FORMULA T2 FORMULA CALCULATION FOR TARGET REFRACTION T2 FORMULA CALCULATION FOR EMMETROPIA MEAN 12,94 Diopters 10,26 Diopters S. DEVIATION 2,889 D 3,061D MINIMUM 5,32 D 0,7039D MAXIMUM 17,85 D 15,12 D n= 55 cases, Source: Database of clinical records, Ophthalmology department, Hadassah Ein Keren Hospital, Jerusalem Israel. 24

25 Table Number 4: IOL POWER CALCULATION USING T2 FORMULA + OPTIMIZED CONSTANT T2 FORMULA + OPTIMIZED CONSTANT (119,0) FOR TARGET REFRACTION MEAN 13,17 10,44 T2 FORMULA + OPTIMIZED CONSTANT (119,0) FOR EMMETROPIA S. DEVIATION 2,929 3,114 MINIMUM 5,41 0,71 MAXIMUM 18,15 15,37 n= 55 cases, Source: Database of clinical records, Ophthalmology department, Hadassah Ein Keren Hospital, Jerusalem Israel. Table Number 5: IOL POWER CALCULATION USING THE SRK/T FORMULA WITH Optimized constant (119,0) SRK/T FORMULA WITH OPTIMIZED CONSTANT (119,0) FOR TARGET REFRACTION SRK/T FORMULA WITH OPTIMIZED CONSTANT (119,0) FOR EMMETROPIA MEAN 13,16 Diopters 10,42 Diopters S. DEVIATION 2,869 D 3,088 D MINIMUM 6,109 D 0,8591 D MAXIMUM 18,14 D 15,16 D n= 55 cases. Source: Database of clinical records, Ophthalmology department, Hadassah Ein Keren Hospital, Jerusalem Israel. Table Number 6 IOL POWER CALCULATION USING THE HOLLADAY 1 FORMULA HOLLADAY FORMULA FOR HOLLADAY FORMULA FOR TARGET REFRACTION EMMETROPIA MEAN 12,66 9,997 S. DEVIATION 3,09 3,269 MINIMUM 4,701 0,2833 MAXIMUM 18,22 15,24 n= 55 cases, Source: Database of clinical records, Ophthalmology department, Hadassah Ein Keren Hospital, Jerusalem Israel. 25

26 Table N. 7 Summary of IOL calculation using 3 optimized constants with the SRK/T formula. Optimized Constants for the IQ IOL according to keratometry. 43 : ,7 : ,7 : Emmetropic IOL Mean: (SD 3.112, min: max: 15.38) Target refraction IOL Mean: (SD 2.89, min: max: 18.22) Median Absolute Error 0,3104 Mean Absolute Error 0,4538 Mean Numerical Error -0,1005 Minimum Value 0,00926 Maximum Value 2,084 Error group 0,00-0,25 D 0,25 0,50 D 0,50-1,00 D 1,00 2,00 D 2,00 Percentage / Number 69,09 % / % / 11 7,27 % / 4 1,81 % / 1 1,81 % / 1 n= 55 cases. Source: Database of clinical records, Ophthalmology department, Hadassah Ein Keren Hospital, Jerusalem Israel 26

27 Table N. 8 Comparison of IOL calculation formulas for Myopic eyes regarding their Error METHOD MEDIAN ABSOLUTE ERROR MEAN NUMERICAL ERROR MEAN ABSOLUTE ERROR ABSOLUTE ERROR MINIMUM VALUE ABSOLUTE ERROR MAXIMUM VALUE SRK/T 0,3-0,048 0, ,965 T2 0,33 0,044 0,5039 0, ,0776 SRK/T WITH OPTIMIZED CONSTANT T2 WITH OPTIMIZED CONSTANT HOLLADAY 1 WITH OPTIMIZED CONSTANT SRK/T 3 A PERSONALIZED CONSTANTS 0,2753-0,081 0,4565 0, ,0583 0,3872-0,10 0,4929 0, ,174 0,3883 0,23 0,5138 0, ,5813 0,3104-0,1005 0, n= 55 cases. Source: Database of clinical records, Ophthalmology department, Hadassah Ein Keren Hospital, Jerusalem Israel. 27

28 Table N. 9 Correlation and Concordance Coefficient of Lin regarding the Absolute Error using different IOL calculation methods ( 95% Confidence Interval) METHOD SRKT T2 SRK/T + OPTIMIZED CONSTANT T2 + OPTIMIZED CONSTANT HOLLADAY 1 WITH OPTIMIZED S.F. SRK/T 3 PERSONALIZED A CONSTANTS SRK/T 0,77 (95% CI 0,64 to 0,86) 0,80 (95% CI 0,68 to 0,88) 0,73 (95% CI 0,59 to 0,84) 0,70 (95% CI 0,54 to 0,82) 0,7753 (95%CI 0,6437 to 0,8623) T2 0,90 (95% CI 0,83 to 0,94) 0,93 (95% CI 0,89 to 0,96) 0,80 (95% CI 0,68 to 0,88) 0,9112 (95% CI: 0,8530 to 0,9470) SRK/T + OPTIMIZED CONSTANT 0,91 (95% CI 0,85 to 0,95) 0,78 (95% CI 0,65 to 0,87) 0,9672 (95% CI: 0,9446 to 0,9807) T2 + OPTIMIZED CONSTANT 0,72 (95% CI 0,56 to 0,82) 0,9596 (95% CI:0,9320 to 0,9761) HOLLADAY 1 WITH OPTIMIZED SURGEON FACTOR 0,7494 (95% CI: 0,6071 to 0,8451) n= 55 cases. Source: Database of clinical records, Ophthalmology department, Hadassah Ein Keren Hospital, Jerusalem Israel. 28

29 Table N. 10 Comparison of the correlation between the Absolute error from various methods for IOL calculation and the Mean Keratometry, in myopic eyes. METHOD Pearson correlation coefficient (Absolute error and Mean K) p value SRK/T 0,089 0,517 SRK/T+OPTIMIZED CONSTANT 0,0051 0,970 T2 0,134 0,329 T2 + OPTIMIZED CONSTANT -0,017 0,903 HOLLADAY 1 OPTIMIZED S.F. -0,0114 0,934 SRK/T+3 O. CONSTANTS -0,012 0,93 n= 55 cases. Source: Database of clinical records, Ophthalmology department, Hadassah Ein Keren Hospital, Jerusalem Israel 29

30 Table N. 11 A Median absolute error for different IOL Calculation methods related to the Mean Keratometric values. Mean Keratometry Absolute Error T2 Absolute Error SRK/T Absolute Error Holladay 1 with Optimized Surgeon Factor Absolute Error SRK/T + Optimized A Constant Absolute Error T2 + Optimized A Constant Absolute Median Absolute Error SRK/T 3 O.C. N D 0,3192 min 0,04 max: 1,45 0,3075 min:0,045 max: 1,25 0,285 min:0,085 max:1,476 0,243 min:0,111 max:1,386 0,4814 min:0,025 max:1,597 0,337 min:0,029 max:1, ,7 D 0,311 min: 0,010 max: 2,078 0,315 min: 0 max: 1,965 0,4535 min: 0,026 max: 1,58 0,2645 min: 0,010 max: 2,058 0,3629 min:0,0066 max:2,174 0,314 min:0,0377 max:2, ,7 D 0,3863 min:0,060. max1,35 0,2625 min:0. max:1,59 0,3371 min: 0,022 max: 1,41 0,2981 min: 0,028 max: 1,74 0,4018 min:0,012 max: 1,53 0,3037 min:0,009 max:1,56 18 Total n= 55 cases. Source: Database of clinical records, Ophthalmology department, Hadassah Ein Keren Hospital, Jerusalem Israel 30

31 Table N. 11 B Median absolute error for different IOL Calculation methods related to the Mean Keratometric values. Mean Keratometry Median Absolute Error T2 Median Absolute Error SRK/T Median Absolute Error Holladay 1 + O. S.F. Median Absolute Error SRK/T + O. C. Median Absolute Error T2+ O. C. Median Absolut e Error SRK/T 3 O.C. N D 0,365 0,2375 0,5409 0,2601 0,5175 0, D 0,3125 0,3150 0,3404 0,264 0,38 0, D 0,373 0,450 0,455 0,2753 0,230 0, D 0,4928 0,225 0,355 0,22 0,387 0,30 5 Total n= 55 cases. Source: Database of clinical records, Ophthalmology department, Hadassah Ein Keren Hospital, Jerusalem Israel 31

32 Table N. 12 Comparison of the correlation between the Absolute error from various methods for IOL calculation and the Axial length, in myopic eyes. METHOD Pearson correlation coefficient (Absolute error and Axial Length ) p value SRK/T 0,0091 0,947 SRK/T+OPTIMIZED CONSTANT 0,075 0,584 T2-0,0429 0,756 T2 + OPTIMIZED CONSTANT 0,0832 0,546 HOLLADAY 1 OPTIMIZED S.F. 0,1136 0,409 SRK/T + 3 OPTIMIZED PERSONALIZED CONSTANTS 0,088 0,52 n= 55 cases. Source: Database of clinical records, Ophthalmology department, Hadassah Ein Keren Hospital, Jerusalem Israel 32

33 Axial length (mm) Table N. 13 Median absolute error for different IOL Calculation methods related to the Axial Length values. Median Absolute Error T2 Median Absolute Error SRK/T Median Absolute Error Holladay 1 O. S.F Median Absolute Error SRK/T Optimized Constant Median Absolute Error T2 Optimized Constant Median Absolute Error SRK/T, 3 Optimized Constants N ,3134 0,1775 0,1834 0,104 0,1899 0, ,33 0,315 0,4535 0,294 0,4806 0, ,351 0,43 0,4552 0,4746 0,4171 0, ,2874 0,3 0,3897 0,3577 0,4543 0, ,608 0,41 0,1086 0,4744 0,6983 0, , ,205 0,7757 0,1596 0, ,140 1 n= 55 cases. Source: Database of clinical records, Ophthalmology department, Hadassah Ein Keren Hospital, Jerusalem Israel 33

34 Table N 14. Comparison of the present study with other studies calculating IOL for Highly Myopic Eyes. Study IOL Calculation methods included Results Number of cases Youngsub Eom, MD, Su-Yeon Kang, MD,et al Use of Corneal Power-Specific Constants to Improve the Accuracy of the SRK/T Formula Ophthalmology 2013;120: SRK/T formula with IOL constant optimization according to the keratometric power values, 1 to 3 optimized constants used, IQ and AO IOL s used. A constants: <43.0D: D- 44.7D: >44,7D: K 43.2 or 45.2 D MedAE 3 constants: 0, 24 All cases: 123, extreme K cases: 62 Sheard Richard, MA, FRCOphth,. Smith Guy T, FRCOphth,. Cooke David L, MD, Improving the prediction accuracy of the SRK/T formula: The T2 formula, J Cataract Refract Surg 2010; 36: SRK/T formula with optimized constant, T2 formula. A constant optimized for SN60WF of 118,97, IOLs included: SN60AT, SN60AT, and others. Mean absolute error of SRK/T with optimized constant: 0,3229 and of T2 with optimized constant: 0,3064. All cases: , SN60WF IOL cases: 6914 Li Wang, MD, PhD, Mariko Shirayama, MD, et al, Optimizing intraocular lens power calculations in eyes with axial lengths above 25.0 mm, J Cataract Refract Surg 2011; 37: Holladay1, Haigis, SRK/T, Hoffer Q. Axial Length optimization, IOLs included: SN60WF, SN60AT, SN60T, MA60MA. MNE with manufacturer s formula, SN60 IOL, Holladay 1: 0,56 SRK/T: 0,27 Haigis 0,68 Hoffer Q 0,68 MAE with optimized AL and MedAE Holladay1:0,43;0,40 SRK/T: 0,47; 0,41 Haigis: 0,36; 0,29 Hoffer Q: 0,51; 0,42 All cases= 94 SN60WF= 55 cases Present study SRK/T, SRK/T 1 Optimized A Constant (119,0); SRK/T 3 Optimized A Constants ( <43.0D: D-44.7 D : >44,7 D: T2 formula, T2 formula with Optimized A Constant (119,0), Holladay 1 with Optimized S. F. (1,84). IOL: SN60WF IQ Method:MedAE/MNE/MAE. SRK/T:0,3/-0,048/0,47 SRK/T 1 Optimized constant:0,27/-0,081/0,45 SRK/T 3 Optimized constants:0,31/-0,10/0,45 T2: 0,33/0,044/0,50 T2 1 Optimized constant:0,38/- 0,10/0,49 Holladay 1 Optimized S.F: 0,38/0,23/0,51 All cases = 55 n= 55 cases. Source: Database of clinical records, Ophthalmology department, Hadassah Ein Keren Hospital, Jerusalem Israel, MedAE: Median absolute error, MAE: Mean absolute error,mne: Mean numerical error 34

35 Graph Number 1: Mean Numerical Error from the methods used in the present study SRK/T 3 OPTIMIZED A CONSTANTS -0,1005 T2 AND OPTIMIZED CONSTANT -0,1094 Graph N. 1, Mean Numerical Error SRK/T AND 1 OPTIMIZED CONSTANT -0,08095 HOLLADAY1 0,2323 T2 0, ,04882 SRK/T -0,15-0,1-0,05 0 0,05 0,1 0,15 0,2 0,25 n= 55 cases. Source: Database of clinical records, Ophthalmology department, Hadassah Ein Keren Hospital, Jerusalem Israel. 35