Corneal Refractive Power Estimation and Intraocular Lens Calculation after Hyperopic LASIK Shady T. Awwad, MD,1,2 Patrick S. Kelley, MD,1 R. Wayne Bowman, MD,1 H. Dwight Cavanagh, MD, PhD,1 James P. McCulley, MD1 Purpose: To identify key independent variables in estimating corneal refractive power (KBC) after hyperopic LASIK. Design: Retrospective study. Participants: We included 24 eyes of 16 hyperopic patients who underwent LASIK with subsequent phacoemulsification and posterior chamber intraocular lens (IOL) implantation in the same eye. Methods: Pre-LASIK and post-LASIK spherical equivalent (SE) refractions and topographies, axial length, implant type and power, and 3-month postphacoemulsification SE were recorded. Using the double-K Hoffer Q formula, corneal power was backcalculated for every eye (KBC), regression-based formulas derived, and corresponding IOL powers calculated and compared with published methods. Main Outcome Measures: The Pearson correlation coefficient (PCC) and arithmetic and absolute corneal and IOL power errors. Results: Adjusting either the average central corneal power (ACCP3mm) or SimK based on the laser-induced spherical equivalent change (⌬SE) resulted in an estimated corneal power (ACCPadj and SimKadj) with highest correlation with KBC (PCC ⫽ 0.940 and 0.956, respectively) and lowest absolute corneal estimation error (0.37⫾0.45 and 0.38⫾0.39 diopter [D], respectively). The ACCPadj closely mirrored published ⌬SE-based adjustments of central corneal power on different topographers, whereas ⌬SE-based SimK adjustments varied across platforms. Using ACCPadj or SimKadj in the double-K Hoffer Q, using ACCP3mm or SimK in single-K Hoffer Q and adjusting the resultant IOL power based on ⌬SE, or applying Masket’s formula all yielded accurate and similar IOL powers. The Latkany method consistently underestimated IOL power. The Feiz–Mannis and clinical history methods yielded poor IOL correlations and large IOL errors. Conclusion: After hyperopic LASIK, adjusting either corneal power or IOL power based on ⌬SE accurately estimates the appropriate IOL power. Financial Disclosure(s): Proprietary or commercial disclosure may be found after the references. Ophthalmology 2009;116:393– 400 © 2009 by the American Academy of Ophthalmology.
Determination of the refractive corneal power after laser keratorefractive surgery has been the subject of numerous studies over the past decade.1–11 Fortunately, continuous clinical research that spurred creation and refinement of formulas, along with newer imaging systems, have helped to improve refractive outcomes.12–14 Most published works, however, have targeted patients with previous myopic keratorefractive surgery; there are few data on corneal power estimation and intraocular lens (IOL) power calculation after hyperopic keratorefractive surgery.15–17 Using the double-K IOL formula concept, we have used data from patients who have undergone cataract extraction after hyperopic LASIK to backcalculate the ideal refractive corneal power and performed multiple regression analysis to identify key variables with their corresponding formulas that would best predict corneal refractive power (KBC) in an accurate, and most important, reproducible manner. © 2009 by the American Academy of Ophthalmology Published by Elsevier Inc.
Patients and Methods A retrospective chart review was conducted to locate patients with a history of hyperopic LASIK who subsequently underwent phacoemulsification and posterior chamber IOL implantation in the same eye between January 2001 and June 2006 at the University of Texas Southwestern Medical Center at Dallas. All patients had to have full prephacoemulsification refractive history, comprising pre-LASIK keratometry (Kpre-LASIK), pre-LASIK refraction, postLASIK refraction before cataract development, and post-LASIK topography. Exclusion criteria included vitreoretinal or corneal disease, history of any other ocular surgery, as well as uveitis, trauma, or systemic diseases affecting vision, and intraoperative complications. Data on 25 eyes could be located, with a total of 24 eyes of 16 patients meeting the criteria and being included in the study. All eyes had a corneal topography using the Topography Modeling System (TMS, Tomey Inc, Phoenix, AZ), and axial length measurement with optical coherence interferometry using the IOLMaster (Carl Zeiss GmbH, Jena, Germany). The 3-month ISSN 0161-6420/09/$–see front matter doi:10.1016/j.ophtha.2008.09.045
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Ophthalmology Volume 116, Number 3, March 2009 postcataract surgery spherical equivalent refraction (SEPCE), type and power of the implanted IOL, axial length, and topographic data extracted from the TMS topographer, simulated keratometry (SimK) and average central corneal power over the central 3 mm of the cornea (ACCP3mm), were all recorded. The ACCP3mm is the average of the mean powers of the central placido rings over the central 3 mm area, and is analogous to the effective refractive power of the cornea (EffRP) available on the Holladay Diagnostic Summary on the EyeSys topographer, without the Stiles-Crawford compensation effect, and similar to the annular central power (AnnCP) on the Humphrey topographer.3,17,18 The types of IOL implanted were AcrySof SA60AT and SN60AT, AcrySof IQ, and AcrySof Restor (Alcon Labs, Fort Worth, TX). Cataract surgeries were performed by RWB, HDC, and JPM, and the IOL constants optimized for the partial coherence interferometery method of axial length measurement. Laser correction surgery was performed using the VISX S2, S3, and S4 systems (VISX, Santa Clara, CA) with an optical zone of 6.0 mm and a transition zone of 8.5 mm. The study was performed with the approval of the University of Texas Southwestern Medical Center Institutional Review Board and in accordance with the Declaration of Helsinki guidelines for human research and the Health Insurance Portability and Accountability Act. Two types of methods are currently available to calculate IOL power in postkeratorefractive eyes. One method adjusts the measured corneal power, and then uses the adjusted value in a double-K modified IOL formula. The second method simply inputs the measured corneal power in a single-K IOL formula, and then adjusts the resultant IOL power according to the laser induced refractive change.
Regression Analysis Derivation: Corneal Power Adjustment For each eye, the ideal KBC was backcalculated using the double-K Hoffer Q formula and the 3-month SE, the implanted IOL power and constant, and axial length. The KBC was considered the gold standard, and both corneal power measurements, ACCP3mm and simulated K (SimK) were adjusted according to KBC using multiple regression analyses of the form Y ⫽ aX ⫹ bZ ⫹ C, where Y represents the dependent variable and is KBC, and X and Z are independent variables. X and Z can include either ACCP3mm or SimK, together with the laser-induced SE change: pre-LASIK SE (SEpre-LASIK) ⫺ post-LASIK SE (SEpost-LASIK). Four regression analyses were created based on 4 sets of parameters: 1. 2. 3. 4.
KBC and ACCP3mm KBC and SimK KBC, ACCP3mm, and (SEpre-LASIK ⫺ SEpost-LASIK) KBC, SimK, (SEpre-LASIK ⫺ SEpost-LASIK)
Regression Analysis Derivation: Intraocular Lens Power Adjustment To compare to published formulas that adjust the final IOL power calculated from single-K third-generation formulas, bypassing corneal power adjustment (the Masket and Latkany methods), regression analyses were created based on IOL power adjustment. In this scenario, the implanted IOL power (IOLi) was considered the gold standard, and the resulting postphacoemulsification spherical equivalent (SEPCE) was used as the target correction to calculate the IOL power via the single-K Hoffer Q formula. The calculated IOL power was then adjusted by regression analysis according to the laser-induced refractive change. For every eye, 2 values of IOL power were calculated, IOLACCP3mm and IOLSimK, depending on
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whether ACCP3mm or SimK were used in the single-K formula, hence leading to 2 more regression formulas with the following parameters: 5. IOLi, IOLACCP3mm, and (SEpre-LASIK ⫺ SEpost-LASIK) 6. IOLi, IOL SimK, and (SEpre-LASIK ⫺ SEpost-LASIK) The first 4 regression formulas were used in every eye to compute the corresponding refractive corneal power, which was compared with KBC. For each formula, the Pearson correlation coefficient was calculated, and the corneal power estimation error was calculated as such: Arithmetic corneal power estimation error ⫽ estimated corneal power ⫺ KBC The absolute corneal power estimation error was derived using the absolute value of the arithmetic corneal power estimation error. The proportion of eyes within ⫾ 1.0 diopters (D) of corneal power error was evaluated. The results were compared with the clinical history method (CHM). For the CHM, the pre-LASIK and postLASIK spherical equivalents (SEpre-LASIK and SEpost-LASIK) were converted to the corneal plane, and then the difference in SE was subtracted from the pre-LASIK keratometric value to obtain the refractive power (KCHM).12 The last 2 regression formulas (5 and 6) were also used in every eye to compute the corresponding IOL (IOLc), which was compared with the IOLi, with the IOL power estimation error being equal to (IOLc ⫺ IOLi). For every formula, the Pearson correlation coefficient, the arithmetic and absolute IOL power estimation error, and the proportion of eyes within ⫾ 1.0 D of IOL power error were calculated. The results were compared with available methods for computing and adjusting IOL power after posthyperopic keratorefractive surgery, and assuming the postoperative refraction target to be equal to the actual postoperative spherical equivalence in each case (SEPCE). The latter formulas included the Feiz–Mannis,5,16 modified Feiz–Mannis,16 Masket,7 modified Masket (Hill WE. IOL power calculation after keratorefractive surgery. Paper presented at: the Annual Meeting of the American Society of Cataract and Refractive Surgery, San Francisco, California, March 2006), and Latkany method.16 These methods all use the single-K IOL formulas and are summarized below. 1. Feiz–Mannis method: IOL is computed using Kpre-LASIK as the corneal power value, then is adjusted using the following correction factor: (SEpre-LASIK ⫺ SEpost-LASIK)/0.7; hence, IOL ⫽ IOL Kpre-LASIK ⫺ (SEpre-LASIK ⫺ SEpost-LASIK)/0.7. 2. Modified Feiz–Mannis method: Similar to the original method, the modified formula is theoretically more exact, in that the laser-induced change in spherical equivalence is input as the target refraction in the IOL formula. Kpre-LASIK is still used as the corneal power value. 3. Masket method: IOL ⫽ IOLSimK ⫺ 0.326 ⫻ (LSE) ⫹ 0.101, where LSE is the vertex distance corrected laser vision correction SE. 4. Modified Masket method: IOL ⫽ IOLSimK ⫺ 0.4385 ⫻ LSE ⫹ 0.0295. 5. Latkany method: IOL ⫽ IOLSimK ⫺ (0.27 ⌬SE ⫹ 1.53), where ⌬SE is the difference between preoperative and postoperative spherical equivalents (SE pre-LASIK ⫺ SEpost-LASIK). The Feiz–Mannis and modified Feiz–Mannis methods bypass the problem of the effective lens position (ELP) estimation error by using the Kpre-LASIK for the corneal power in the single-K IOL
Awwad et al 䡠 IOL Calculations after Hyperopic LASIK formula and adjusting with laser-induced change in refraction. As for the Masket and Latkany methods, both use the single-K IOL formula and account for both the corneal power estimation error and the ELP estimation error by adjusting the IOL power based on the laser-induced refractive change. The double-K adjustment of the original Hoffer Q formula with its updated errata and with its derivation of the backcalculated refraction was carefully programmed in Excel and is detailed in Appendix 1 (available online at http://aaojournal.org).19 The Hoffer Q formula, as programmed in Excel, was tested against the Hoffer Q formula programmed in the Holladay IOL Consultant software (officially licensed to calculate Hoffer Q formula) using SimK as the default corneal power with and without double-K adjustment and results were found to match for all eyes. The Excel version was subsequently used to run simultaneous tandem calculations on all eyes using different parameters each time and to integrate the data efficiently for statistical analysis. The statistical data in Excel was exported to Sigmastat software (Jandel Scientific, San Rafael, CA) for analysis. The paired Student t-test (2-tailed distribution) was used to compare the algebraic and absolute IOL errors, and the McNemar test for nonparametric analysis of related samples was used to compare proportions between related groups. P⬍0.05 was considered significant.
Patient Demographics and Characteristics The average patient age was 62.5⫾7.13 years. The axial length measurements averaged 22.91⫾0.58 mm, ranging from 22.10 to 23.81 mm. The average of the effective refractive correction (⌬SE ⫽ SEpre-LASIK ⫺ SEpost-LASIK), which takes into consideration the refractive regression effect, was 2.34⫾0.95 D (range, ⫹0.25 to ⫹3.87 D).
Regression Formulas Regression analysis using KBC as the dependent variable and different combinations of independent variables yielded the following equations: [1]
and SimK' ⫽ 0.917 ⫻ SimK ⫹ 4.016 (r2 ⫽ 0.895; P⬍0.001). [2] Both formulas are roughly 90% of the K reading plus 4: ACCPadj ⫽ 0.857 ACCP3mm ⫹ 0.242 (SEpre-LASIK ⫺ SEpost-LASIK) ⫹ 6.021 (r2 ⫽ 0.888; P⬍0.001). Using KBC ⫺ ACCP3mm as a dependent variable, we get: ACCPadj ⫺ ACCP3mm ⫽ 0.144 (SEpre-LASIK ⫺ SEpost-LASIK) ⫺ 0.256. Hence, the equation: ACCPadj ⫽ ACCP3mm ⫹ 0.144 (SEpre-LASIK ⫺ SEpost-LASIK) ⫺ 0.256 [3] SimKadj ⫽ 0.864 SimK ⫹ 0.255 (SEpre-LASIK ⫺ SEpost-LASIK) ⫹ 5.826 (r2 ⫽ 0.914; P⬍0.001). Using KBC ⫺ SimK as a dependent variable, we get:
Hence, the equation: SimKadj ⫽ SimK ⫹ 0.165 (SEpre-LASIK ⫺ SEpost-LASIK) ⫺ 0.105.
[4]
A regression analysis bypassing the double-K method was also devised with IOLi ⫺ IOLACCP3mm, taken as the dependent variable, and ⌬SE as the independent variable (IOLACCP3mm being the IOL power derived via the single-K Hoffer Q formula and using ACCP3mm as the corneal power): IOLi ⫺ IOLACCP3mm ⫽ ⫺0.350 ⌬SE ⫹ 0.085 IOLadj_ACCP ⫽ IOLACCP3mm ⫺ 0.35 ⌬SE ⫹ 0.085
[5]
Another regression analysis bypassing the double-K method, that could be used when Kpre-LASIK is unknown, was also devised with IOLi ⫺ IOLSimK, taken as the dependent variable, and ⌬SE as the independent variable (IOLSimK being the IOL power derived via the single-K Hoffer Q formula and using SimK as the corneal power): IOLi ⫺ IOLSimK ⫽ ⫺0.359 ⌬SE ⫹ 0.092. IOLadj_SimK ⫽ IOLSimK ⫺ 0.359 ⌬SE ⫹ 0.092
Results
ACCP' ⫽ 0.909 ⫻ ACCP3mm ⫹ 4.198 (r2 ⫽ 0.874; P⬍0.001);
SimKadj ⫺ SimK ⫽ ⫹0.165 (SEpre-LASIK ⫺ SEpost-LASIK) ⫺ 0.105
[6]
The Pearson Correlation Coefficient and Arithmetic and Absolute Refractive Corneal Power Estimation Errors The Pearson correlation coefficients for the estimated refractive corneal power derived using the different regression formulas and the arithmetic and absolute errors are summarized in Table 1, together with their corresponding arithmetic and absolute corneal power estimation error. ACCP3mm approximated the refractive corneal power slightly better than SimK, which tended to underestimate it (arithmetic and absolute corneal power of ⫺0.082⫾ 0.61 and 0.41⫾0.44, respectively, vs ⫺0.28⫾0.55 and 0.48⫾0.39, respectively, for SimK). On the other hand, SimK had a slightly better Pearson correlation with the refractive corneal power represented by KBC than ACCP3mm (0.946 vs 0.935, respectively). Regression analyses based on SimK and ⌬SE (SEpre-LASIK ⫺ SEpost-LASIK), (SimKadj; equation 4), yielded the highest correlation coefficients (0.956), followed by regression based on SimK alone (SimK=; equation 2; 0.946), and regression based on ACCP3mm and ⌬SE (ACCPadj; equation 3; 0.940). The CHM yielded the lowest correlation with only 0.821. The SimKadj improved the correlation and the arithmetic and absolute corneal power error of SimK (⫺0.28⫾0.55 vs 0.00⫾0.53 [P⬍0.001] and 0.38⫾0.39 vs 0.48⫾0.39 [P ⫽ 0.09], respectively; Table 1). Similarly, ACCPadj improved on the correlation and the absolute error of ACCP3mm, although the difference in absolute error was not significant (P ⫽ 0.170; Table 1). The difference in absolute error between ACCPadj and SimKadj was not significant (0.37⫾0.45 vs 0.38⫾0.39; P ⫽ 0.929). The CHM yielded the largest absolute corneal power estimation error (0.72⫾0.63), which was statistically significant when compared with the error of SimKadj and ACCPadj (P⬍0.001 for both). Table 2 summarizes the percentage of eyes within a certain corneal power estimation error for all the formulas. Only 83% and 92% of CHM eyes lay within ⫾ 1.5 D and ⫾ 2.0 D of error, as opposed to 96% to 100% and 100% for ACCP3mm, SimK, or the rest of the regression formulas. The difference, however, was not significant. The adjustments that need to be made on the TMS topographic measurements ACCP3mm and SimK based on the laser treated
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Ophthalmology Volume 116, Number 3, March 2009 Table 1. Arithmetic and Absolute Corneal Power Estimation Errors of the Different Derived Regression, as well as the Historical K Method, and the Pearson’s Correlation (r) of Their Respective Derived Corneal Power with the Backcalculated Corneal Power for Each Eye (Kbackcalc) Regression Formulas and Corneal Power Estimation Methods
Arithmetic Corneal Power Estimation Error (D)
Absolute Corneal Power Estimation Error (D)
Pearson’s Correlation*
⫺0.082⫾0.61 ⫺0.28⫾0.55 ⫺0.018⫾0.59 ⫺0.020⫾0.53 0.000⫾0.59 0.000⫾0.53 0.18⫾0.94
0.41⫾0.44 0.48⫾0.39 0.40⫾0.41 0.41⫾0.35 0.37⫾0.45 0.38⫾0.39 0.72⫾0.63
0.935 0.946 0.935 0.946 0.940 0.956 0.821
ACCP3mm SimK Regression based on ACCP Regression based on SimK ACCPadj SimKadj Clinical history method
ACCPadj ⫽ Regression based on ACCP3mm and ⌬ SE; ACCP3mm ⫽ average central corneal power within the central 3 mm; D ⫽ diopters; ⌬SE ⫽ change in spherical equivalent refractions (SEpre-LASIK ⫺ SEpost-LASIK); SimK ⫽ simulated keratometric value; SimKadj ⫽ regression based on SimK and ⌬SE. *P⬍0.0001 for all.
correction are detailed in Table 3, with the adjustments published by Wang et al for phakic eyes posthyperopic keratorefractive surgery listed in parallel for comparison purposes.15 As can be seen, the adjustments on the ACCP3mm are strikingly similar to those of EffRP and AnnCP, which are similar indices of the average central corneal power on the EyeSys and Atlas topographers, respectively. On the other hand, the SimK adjustments seem to be dependent of the topography platform used (Table 3).
Comparison with Published Posthyperopic Keratorefractive Surgery Intraocular Lens Power Calculation Methods The Pearson correlation and the arithmetic and absolute IOL power errors of the derived regression formulas and the published IOL power calculation methods for eyes after hyperopic keratorefractive surgery are summarized in Table 4. Performing corneal adjustment based on ACCP3mm and ⌬SE (ACCPadj; equation 3) or SimK and ⌬SE (SimKadj; equation 4) and using the calculated
Table 2. Percentage of Eyes with Corneal Power Estimation Error within a Certain Range, as a Function of Topographic Parameters, Regression Formulas, as well as the Historical K Method, in Eyes with Previous Hyperopic Keratorefractive Surgery Percentage of Eyes within a Certain Corneal Power Estimation Error
Refractive Corneal Power Estimation Methods
⫾ 0.5 D
⫾ 1.0 D
⫾ 1.5 D
⫾ 2.0 D
ACCP3mm SimK Regression based on ACCP Regression based on SimK ACCPadj SimKadj Clinical history method
75 62 75 75 75 75 46
83 92 92 83 88 92 79
96 96 100 100 96 96 83
100 100 100 100 100 100 92
ACCP3mm ⫽ average central corneal power within the central 3 mm; ACCPadj ⫽ regression based on ACCP3mm and ⌬SE; D ⫽ diopters; SimK ⫽ simulated keratometric value; SimKadj ⫽ regression based on SimK and ⌬SE; ⌬SE ⫽ change in spherical equivalent refractions (SEpre-LASIK ⫺ SEpost-LASIK).
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value in the double-K Hoffer Q formula resulted in a similar Pearson correlation and arithmetic and absolute errors compared with the Masket method (Table 4), and better Pearson correlation as well as smaller arithmetic and absolute IOL power estimation errors than the CHM (P ⫽ 0.367 and P ⫽ 0.362, respectively, for arithmetic error; P ⫽ 0.013 and P ⫽ 0.007 for absolute error), Feiz–Mannis/double-K Hoffer Q (P⬍0.001 for both, in arithmetic and absolute errors), modified Masket method (P⬍0.001 for both, in arithmetic and absolute errors), as well as the modified Latkany method (P⬍0.001 for both, in arithmetic and absolute errors), all of which, except CHM, were derived from a regression-based adjustment of IOL power using the single-K Hoffer Q formula (Table 4). The Latkany method resulted in a systematic underestimation of the IOL power, as shown by the arithmetic IOL error, which was about equal in value to the absolute IOL error (Fig 1). On the other hand, the modified Masket method resulted in slight overestimation of the IOL power (Fig 1). IOL calculation using ACCP3mm and the single-K Hoffer Q and subsequent adjustment based on ⌬SE (IOLadj_ACCP; equation 5) had an arithmetic and absolute IOL power error of 0.01⫾0.76 and 0.50⫾0.57 D, essentially similar to ⫺0.07⫾0.76 and 0.53⫾0.54 D obtained by the double-K Hoffer Q using adjusted corneal power based on ACCP3mm and ⌬SE (ACCPadj; equation 3; P ⫽ 0.805 and P ⫽ 0.646, respectively; Table 4; Fig 2). In addition, IOL calculation using SimK and the single-K Hoffer Q and subsequent adjustment based on ⌬SE (IOLadj_SimK; equation 6) had an arithmetic and absolute IOL power error of 0.00⫾0.79 and 0.52⫾0.57 D, which compares with the ⫺0.05⫾0.80 and 0.55⫾0.57 D obtained by the double-K Hoffer Q using adjusted corneal power based on SimK and ⌬SE (SimKadj; equation 4; P ⫽ 0.872 and P ⫽ 0.339, respectively; Fig 3). The percentage of eyes within a certain error range is summarized in Table 5. When using ACCPadj (equation 3) with the double-K Hoffer Q, 92% and 100% of eyes were within ⫾ 1.5 D and ⫾ 2.0 D of IOL power error, respectively, compared with 92% and 96%, respectively, with SimKadj (equation 4) with double-K Hoffer Q, 79% and 83%, respectively, for the Feiz–Mannis and the CHM (P ⫽ 0.125 for both), 92% and 96% for both the Masket and the modified Masket methods (P ⫽ 1.000 for both), and 54% and 79% for the Latkany method (P ⫽ 0.001 and P ⫽ 0.063, respectively). The single-K regression-derived IOL adjustment method IOLadj_ACCP (equation 5) and IOLadj_SimK (equation 6) both had 92% and 96% of eyes within ⫾ 1.5 D and ⫾ 2.0 D of IOL power error, respectively (P ⫽ 1.000 for both; Table 5).
Awwad et al 䡠 IOL Calculations after Hyperopic LASIK Table 3. Adjustment of Measurements from Tomey Topographic Modulation System (TMS) Topographer with Comparison with Adjustment Figures Published by Wang et al on the EyeSys and Atlas Topographers in Eyes after Hyperopic LASIK15 Adjustment for Hyperopic LASIK (D)
LASIK-Induced Refractive Correction (D)
TMS ACCP3mm
TMS SimK
EyeSys EffRP
EyeSys SimK
Atlas AnnCP
Atlas SimK
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
⫺0.18 ⫺0.11 ⫺0.04 0.03 0.10 0.18 0.25 0.32 0.39 0.46 0.54 0.61
⫺0.02 0.06 0.14 0.22 0.31 0.39 0.47 0.56 0.64 0.72 0.80 0.89
⫺0.20 ⫺0.12 ⫺0.04 0.04 0.13 0.21 0.29 0.37 0.45 0.53 0.61 0.69
⫺0.11 0.03 0.18 0.32 0.47 0.61 0.75 0.90 1.04 1.19 1.33 1.48
⫺0.30 ⫺0.20 ⫺0.11 ⫺0.01 0.08 0.18 0.27 0.37 0.46 0.56 0.65 0.75
⫺0.17 0.05 0.26 0.48 0.69 0.91 1.13 1.34 1.56 1.77 1.99 2.21
ACCP3mm ⫽ average central corneal power within the central 3 mm; AnnCP ⫽ Annular central power (3 mm area); D ⫽ diopters; EffRP ⫽ effective refractive power (3 mm area); SimK ⫽ simulated keratometric value.
Discussion Although numerous publications and studies have tackled the problem of IOL calculation and corneal power prediction in eyes after myopic keratorefractive surgery, very few studies have evaluated the IOL and corneal power calculations after hyperopic laser keratorefractive procedures. Wang et al evaluated phakic eyes after hyperopic LASIK without cataract surgery and IOL insertion, and using the CHM as the gold standard, tried to improve the accuracy of the corneal power estimation by taking into consideration the change in spherical equivalence from the laser procedure.15 Two topography systems were used and both SimK and average central corneal powers were evaluated (EffRP
for EyeSys and AnnCP for the Humphrey system); interestingly, the suggested modifications to the measured values, based on regression analysis, were similar between the 2 topographers for the average central corneal power, but different for SimK (Table 3). Most important, the average corneal power modifications derived are very similar to our regression-derived modifications for ACCP3mm on the TMS system (Table 3). On the other hand, Latkany et al recently reported their results on posthyperopic LASIK eyes that underwent phacoemulsification and IOL insertion. Using backcalculation, and only average keratometry and SimK values, they determined that the best predictive IOL formula would rely on the concept of Feiz–Mannis, which also was not statistically
Table 4. Arithmetic and Absolute Intraocular Lens (IOL) Power Estimation Errors of the Regression-Derived Formulas, Compared with Popular Methods to Calculate IOL Power in Eyes after Hyperopic Keratorefractive Surgery, with Their Corresponding IOL Pearson Correlation with the Implanted IOL Power (IOLimplanted) Regression Formulas and IOL Power Estimation Methods Double-K methods ACCPadj and double-K Hoffer Q† SimKadj and double-K Hoffer Q† Historical K and double-K Hoffer Q Single-K methods Feiz–Mannis method Modified Feiz–Mannis method Masket method Modified Masket method Latkany method IOLadjACCP† IOLadjSimK†
Arithmetic IOL Power Estimation Error (D)
Absolute IOL Power Estimation Error (D)
Pearson’s Correlation
⫺0.07⫾0.76 0.05⫾0.80 ⫺0.20⫾1.34
0.53⫾0.54 0.55⫾0.57 0.93⫾0.96*
0.957 0.958 0.788
0.00⫾1.36 ⫺0.17⫾1.41 ⫺0.06⫾0.78 0.28⫾0.79 ⫺1.41⫾0.79* 0.01⫾0.76 0.00⫾0.79
0.99⫾0.90* 1.01⫾0.98* 0.54⫾0.57 0.62⫾0.55 1.45⫾0.71* 0.50⫾0.57 0.52⫾0.57
0.780 0.767 0.956 0.956 0.952 0.958 0.956
ACCP3mm ⫽ average central corneal power within the central 3 mm; ACCPadj ⫽ regression based on ACCP3mm and ⌬SE; D ⫽ diopters; F(x,y) ⫽ regression formula with x and y as dependent variables; IOL power error ⫽ IOLcalculated ⫺ IOLimplanted; ⌬SE ⫽ pre-LASIK ⫺ SEpost-LASIK; SimK ⫽ simulated keratometric value; SimKadj ⫽ regression based on SimK and ⌬SE. *Statistical significance compared to ACCPadj or SimKadj and double-K Hoffer Q. † Formula derived by regression analysis.
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Figure 1. Scatter plot of implanted intraocular lens power (IOLi) versus calculated IOL power (IOLc) using the Masket, Masket modified, and Latkany methods (based on SimK), and the regression-derived single-K IOL adjustment based on average central corneal power (ACCP3mm), (IOLACCP3mm ⫺ 0.53 ⌬SE ⫹ 0.085) in posthyperopic LASIK eyes. D ⫽ diopters; SE ⫽ spherical equivalent.
different from a simplistic SimK-based regression formula they determined to be: IOL⫽ IOLSimK ⫺ (0.27 ⫻ ⌬SE ⫹ 1.53 [the Latkany method]). This formula, together with the SimK-based modified Masket formula, yielded poor results when applied to our patients’ sample. This finding, together with the discrepancies found by Wang et al among SimKbased regression formulas generated from different topographers, indicate that SimK measurements in posthyperopic LASIK eyes are highly platform dependent.15 On the other hand, average central corneal power measurements, such as EffRP (EyeSys), ACCP3mm (TMS), and AnnCP (Humphrey), seem to have little platform dependency, as the adjustments that need to be made to the measured values
Figure 2. Scatter plot of implanted intraocular lens (IOL) power versus calculated IOL power using adjusted average central corneal power (ACCPadj), (ACCP3mm ⫹ 0.144 ⌬SE ⫺ 0.256), and adjusted simulated keratometric values (SimKadj), (SimK ⫹ 0.165 ⌬SE – 0.105), as the post-LASIK K values in the double-K Hoffer Q formula in posthyperopic LASIK eyes. D ⫽ diopters; SE ⫽ spherical equivalent.
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Figure 3. Scatter plot of implanted intraocular lens (IOL) power versus calculated IOL power using regression derived single-K IOL adjustment (IOLACCP3mm ⫺ 0.53 ⌬SE ⫹ 0.085) and the double-K Hoffer Q formula with adjusted average central corneal power (ACCPadj), (ACCP3mm ⫹ 0.144 ⌬SE ⫺ 0.256) as the post-LASIK K value in post hyperopic LASIK eyes. The average laser-induced spherical equivalent change was 2.34⫾ 0.95 diopters (D; range, ⫹0.25 to ⫹3.87 D). SE ⫽ spherical equivalent.
after posthyperopic LASIK eyes are strikingly similar; the average central corneal power adjustments suggested by Wang et al on the EyeSys and Humphrey systems compare rigidly with those derived by our regression analysis on the TMS system (Table 3). It is interesting to note that although the original Masket formula was developed with the majority of included eyes being postmyopic LASIK and only 7 eyes after hyperopic LASIK,7 it yielded nearly similar results when compared with the regressions based on average central corneal power in our patients’ sample. However, because it relies on SimK measurements, the extension of the obtained results to other platforms needs to be verified; the modified Masket formula, for instance, had somehow inferior results in our study sample. As for CHM and Feiz–Mannis methods, they yielded suboptimal results. We believe this is due to the fact that these 2 formulas, although theoretically correct and able to be considered as gold standards, fail to perform well in real life. Many errors could be introduced in pre- and postoperative refraction owing to accommodation, regression, or myopic shift of an early and yet clinically occult cataract. In addition, the error produced in any step is carried to the final postphacoemulsification refraction on a 1:1 basis, unlike regression-based formulas where a coefficient is multiplied by the change in spherical equivalence, hence decreasing the final error and imparting more leeway and forgiveness to the formula. For instance, with ACCPadj ⫽ ACCP3mm ⫹ 0.144 ⌬SE ⫺ 0.256, an error of 1 D in ⌬SE is multiplied by 0.144. Ater hyperopic LASIK, unlike after radial keratotomy and myopic LASIK, results with adjusted SimK were similar to those with adjusted average central corneal power.3,17 However, adjustment based on the latter seems to be universal across all topography platforms, whereas SimK adjustment seems to be machine dependent. Hence, unlike the
Awwad et al 䡠 IOL Calculations after Hyperopic LASIK Table 5. Percentage of Eyes within a Certain Intraocular Lens (IOL) Power Error for the RegressionDerived Formulas, Compared with Popular Methods to Calculate IOL Power in Eyes after Hyperopic Keratorefractive Surgery Percentage of Eyes within a Certain IOL Power Estimation Error IOL Power Prediction Methods Double-K methods ACCPadj and double-K Hoffer Q† SimKadj and double-K Hoffer Q† Historical K and double-K Hoffer Q Single-K methods Feiz–Mannis method Modified Feiz–Mannis method Masket method Modified Masket method Latkany method IOLadjACCP† IOLadjSimK†
⫾ 0.5 D
⫾ 1.0 D
⫾ 1.5 D
⫾ 2.0 D
63 63 46
79 88 67
92 92 79
100 96 83
33* 38 63 54 13* 67 63
67 71 88 83 25* 88 88
79 79 92 92 54* 92 92
83 79 96 96 79* 96 96
ACCP3mm ⫽ average central corneal power within the central 3 mm; ACCPadj ⫽ ACCP3mm ⫹ 0.144 ⌬SE ⫺ 0.256; D ⫽ diopters; IOLadjACCP ⫽ single-K IOLACCP3mm ⫺ 0.35 ⌬SE ⫹ 0.085; IOLadjSimK ⫽ single-K IOLSimK ⫺ 0.359 ⌬SE ⫹ 0.092; ⌬SE ⫽ SEpre-LASIK ⫺ SEpost-LASIK; SimK ⫽ simulated keratometric value; SimKadj ⫽ SimK ⫹ 0.165 ⌬SE – 0.105. *Statistical significance compared to ACCPadj or SimKadj and double-K Hoffer Q. † Formula derived by regression analysis.
Latkany and Masket methods, a regression method that bypasses the double-K concept should seemingly rely on the average central corneal power, not SimK, to be universally applicable on all topographers; this has been proven by our results and those of Wang et al on corneal power estimation.15 Although the original and modified Masket methods use the Hoffer Q for hyperopic eyes with axial length ⬍23.0 mm, the Latkany method was originally described using SRK/T. In our comparison, we used the Hoffer Q for all methods to avoid confounding variables in our comparison and because of its known performance in eyes with short axial length. One limitation of our study is that we did not measure the actual ELP of eyes after phacoemulsification (calculated as measured ACD added to half the IOL thickness). Had the actual true ELP been measured, then the refractive corneal power could have been calculated using the single-K Hoffer Q and it would have been more accurate when compared with the values obtained from using a personalized ACD in the double-K Hoffer Q formula. Another limitation of our study is that our sample size of 24 eyes, although relatively large compared with previous studies on posthyperopic LASIK pseudophakic eyes, is still considered small on a statistical level. In summary, for accurate IOL calculations after hyperopic keratorefractive surgery, we recommend adjusting the average central corneal power according to the induced refractive change ⌬SE (ACCPadj ⫽ ACCP3mm ⫹ 0.144 (SEpre-LASIK ⫺ SEpost-LASIK) ⫺ 0.256 [equation 3]) or as displayed in Table 3, then using the obtained value in the double-K Hoffer Q formula. This method ensures both accurate results and potentially reproducible outcomes among topographers. In the absence of historical data on the
patient’s refractive status, the average central corneal power can be adjusted as such: ACCP= ⫽ 0.909 ⫻ ACCP3mm ⫹ 4.198 (equation 1), then used in the double-K Hoffer Q formula with pre-LASIK keratometric value assumed to be 43.86. If the average central corneal power is not available, we recommend adjusting the SimK according to the refractive change: SimKadj ⫽ SimK ⫹ 0.165 (SEpre-LASIK ⫺ SEpost-LASIK) ⫺ 0.105 (equation 4), and if the refractive change is also missing, then using SimK= ⫽ 0.917 ⫻ SimK ⫹ 4.016 (equation 2) would be appropriate. If the clinician does not have access to the double-K Hoffer Q formula, using the average central corneal power or the SimK values as such in the single-K Hoffer Q formula and adjusting the final IOL power based on the SE seems to be equally accurate: IOLadj_ACCP ⫽ IOLACCP3mm ⫺ 0.35 ⌬SE ⫹ 0.085 and IOLadj_SimK ⫽ IOLSimK ⫻ 0.359 ⌬SE ⫹ 0.092 (equations 5 and 6, respectively). In this scenario, the original Masket formula seems also to perform very well and can be used as well (IOL ⫽ IOLSimK ⫺ 0.326 ⫻ [LSE] ⫹ 0.101). However, it is important to bear in mind that, especially for regression methods using SimK, prior validation on the clinician’s topographer is recommended to confirm reproducibility of the suggested formulas. In addition, although the suggested formulas bypassing the double-K method (including Masket’s formula) seem simple and accurate, it would be wise to await reproducibility on a large sample of eyes before recommending it across the board, because the accuracy of such method for large values of SE changes has not yet been tested. The advent of slit-beam videokeratography with the ability to measure both the anterior and the posterior surface of the cornea seems promising in improving the accuracy of KBC measurement after keratorefractive surgery. In the meantime, relying on accurate, and most importantly, reproducible, regression-derived formulas on
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Ophthalmology Volume 116, Number 3, March 2009 the placido systems after hyperopic keratorefractive surgery is key to satisfactory patients’ outcomes.
10.
References 11. 1. Kalski RS, Danjoux JP, Fraenkel GE, et al. Intraocular lens power calculation for cataract surgery after photorefractive keratectomy for high myopia. J Refract Surg 1997;13: 362– 6. 2. Holladay JT. Corneal topography using the Holladay Diagnostic Summary. J Cataract Refract Surg 1997;23:209 –21. 3. Maeda N, Klyce SD, Smolek MK, McDonald MB. Disparity between keratometry-style readings and corneal power within the pupil after refractive surgery for myopia. Cornea 1997;16: 517–24. 4. Seitz B, Langenbucher A. Intraocular lens calculations status after corneal refractive surgery. Curr Opin Ophthalmol 2000; 11:35– 46. 5. Feiz V, Mannis MJ, Garcia-Ferrer F, et al. Intraocular lens power calculation after laser in situ keratomileusis for myopia and hyperopia: a standardized approach. Cornea 2001;20: 792–7. 6. Wang L, Booth MA, Koch DD. Comparison of intraocular lens power calculation methods in eyes that have undergone LASIK. Ophthalmology 2004;111:1825–31. 7. Masket S, Masket SE. Simple regression formula for intraocular lens power adjustment in eyes requiring cataract surgery after excimer laser photoablation. J Cataract Refract Surg 2006;32:430 – 4. 8. Walter KA, Gagnon MR, Hoopes PC Jr, Dickinson PJ. Accurate intraocular lens power calculation after myopic laser in situ keratomileusis, bypassing corneal power. J Cataract Refract Surg 2006;32:425–9. 9. Ianchulev T, Salz J, Hoffer K, et al. Intraoperative optical refractive biometry for intraocular lens power estimation with-
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Footnotes and Financial Disclosures Originally received: January 8, 2008. Final revision: August 31, 2008. Accepted: September 25, 2008.
Financial Disclosure(s): J.P.M. is a consultant for Alcon Labs, Fort Worth, Texas. Manuscript no. 2008-45.
1
Department of Ophthalmology, University of Texas Southwestern Medical Center, Dallas, Texas.
2
Department of Ophthalmology, American University of Beirut Medical Center, Beirut, Lebanon. Supported in part by an unrestricted grant from Research to Prevent Blindness, New York, New York.
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The authors have no proprietary or commercial interest in materials discussed in this article. Correspondence: James P. McCulley, MD, Department of Ophthalmology, University of Texas Southwestern Medical Center at Dallas, 5323 Harry Hines Blvd. Dallas, Texas 75390-9057. E-mail:
[email protected].
Awwad et al 䡠 IOL Calculations after Hyperopic LASIK
Appendix 1
Equations Equation 1: Anterior chamber depth
Double-K modification of the Hoffer Q Formula Recommended constants:
ACD ⫽ pACD ⫹ 0.3(AL ⫺ 23.5) ⫹ tan(Kpre-LASIK)2 ⫹ (0.1 * M * [23.5 ⫺ AL]2 ⫻ [tan{0.1(G ⫺ AL)2}]) ⫺ 0.99166
Refractive index of cornea ⫽ 1.336 Retinal thickness factor ⫽ 0 Measured and extrapolated values: Kpre-LASIK ⫽ average K-reading before LASIK (D) Kpost-LASIK ⫽ estimated refractive corneal power after LASIK (D) AL ⫽ measured axial length (mm) Chosen values V ⫽ vertex distance of pseudophakic spectacles (mm), default ⫽ 12 mm pACD ⫽ personalized anterior chamber depth constant pACD ⫽ 0.58357 ⫻ A constant ⫺ 63.896 Calculated variables P ⫽ power of the IOL (D) R ⫽ refractive error at corneal plane (D) Rx ⫽ target refractive error at spectacle plane (D)
M: if AL ⱕ 23.00, M ⫽ 1; if AL ⬎ 23 mm, M ⫽ ⫺1 G: if AL ⱕ 23.00, G ⫽ 28.00 mm; if AL ⬎ 23 mm, G ⫽ 23.5 mm If AL ⬎ 31, AL ⫽ 31.0; if AL ⬍ 18.5, AL ⫽ 18.5 Equation 2: Refractive error at corneal plane R ⫽ Rx ⁄ (1 ⫺ 0.012 Rx) Equation 3: Intraocular lens power P ⫽ (1336 ⁄ [AL ⫺ ACD ⫺ 0.05]) ⫺ (1.336 ⁄ [{1.336 ⁄ (Kpost-LASIK ⫹ R)} ⫺ {(ACD ⫹ 0.05) ⁄ 1000}]) Equation 4: Refractive error R ⫽ (1.336⁄ [1.336 ⁄ {1336 ⁄(AL ⫺ ACD ⫺ 0.05) ⫺ P} ⫹ {ACD ⫹ 0.05} ⁄ 1000]) ⫺ Kpost-LASIK Rx ⫽ R ⁄ (1 ⫹ 0.012R)
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