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T and Haigis formulas for predicting corneal astigmatism correction with toric intraocular lenses
ARTICLE
Comparison of SRK/T and Haigis formulas for predicting corneal astigmatism correction with toric intraocular lenses Youngsub Eom, MD, Jong Suk Song, MD, PhD, Yong Yeon Kim, MD, PhD, Hyo Myung Kim, MD, PhD
PURPOSE: To compare the accuracy of the SRK/T and Haigis formulas for predicting corneal astigmatism correction with a toric intraocular lens (IOL). SETTING: Department of Ophthalmology, Korea University College of Medicine, Seoul, South Korea. DESIGN: Retrospective cross-sectional study. METHODS: Eyes with an Acrysof toric IOL were enrolled in the study. The corneal plane effective cylinder power of toric IOLs (target induced astigmatism vector [TIA]) predicted by the SRK/T and Haigis formulas were compared with the cylindrical correction achieved postoperatively (surgically induced astigmatism vector [SIA]). The magnitude of error was defined as the difference between the magnitudes of the SIA and TIA. The median absolute magnitudes of error predicted by the SRK/T and Haigis formulas were compared. The median absolute errors predicted by the 2 formulas were also compared. RESULTS: The mean postoperative SIA was 1.80 diopters (D) G 0.55 (SD). The magnitude of error predicted by the SRK/T and Haigis formulas was 0.31 G 0.40 D and 0.23 G 0.40 D, respectively. The median absolute magnitude of error predicted by the Haigis formula was statistically significantly smaller than that predicted by the SRK/T formula (P < .001). The median absolute error predicted by the Haigis formula (0.35 D) was also statistically significantly smaller than that predicted by the SRK/T formula (0.43 D) (P Z .003). CONCLUSION: The Haigis formula was more accurate than the SRK/T formula not only in predicting the refractive outcome but also in predicting corneal astigmatism correction by toric IOLs. Financial Disclosure: No author has a financial or proprietary interest in any material or method mentioned. J Cataract Refract Surg 2015; 41:1650–1657 Q 2015 ASCRS and ESCRS
Corneal astigmatism is a cause of reduced uncorrected distance visual acuity (UDVA) after cataract surgery.1 Corneal astigmatism can be reduced using a toric intraocular lenses (IOLs), which are effective and perform well in predicting corneal astigmatism correction.2,3 When using toric IOLs, it is important to select patients who are good candidates4 and to be precise when predicting the corneal astigmatism correction. Rotational stability has been the primary focus of many previous studies evaluating toric IOL outcomes5–7; however, because IOL refractive outcomes are affected by the postoperative effective lens position (ELP),8 the corneal plane effective cylinder power of toric IOLs might also be affected by the postoperative 1650
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position. Goggin et al.9 showed that anterior chamber depth (ACD) and pachymetry also affect corneal astigmatism correction by toric IOLs. Savini et al.10 showed that the corneal plane theoretical toricity of toric IOLs varies according to the corneal power (keratometry [K]), ACD, and axial length (AL). Another previous study11 showed that the corneal plane effective cylinder power of toric IOLs was affected by the ELP. Currently, several types of toric IOLs are commercially available with their own online toric IOL calculators. Our institute has used 3 toric IOLs: Acrysof toric (Alcon Laboratories, Inc.), Tecnis toric (Abbott Medical Optics, Inc.), and Zeiss toric (Carl Zeiss Meditec AG). To determine toric IOL cylinder power, the
http://dx.doi.org/10.1016/j.jcrs.2014.12.053 0886-3350
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Abbott Medical Optics (AMO) calculator offers several modes, including the SRK/T formula. The Zeiss calculator provides toric IOL cylinder power based on the Haigis formula. The SRK/T and Haigis formulas suggest different ELPs, using their own methods. Because the corneal plane effective cylinder power of toric IOLs is affected by the ELP,11 the accuracy of prediction of corneal astigmatism correction by toric IOLs might be different between the IOL formulas. This study compared the accuracies of the SRK/T and Haigis formulas for predicting corneal astigmatism correction by toric IOLs. PATIENTS AND METHODS Study Population This retrospective study included eyes in which uneventful phacoemulsification with implantation of an Acrysof SN60T3-T5 (Alcon Laboratories, Inc.) toric IOL 1.50 to 3.00 diopters (D) cylinder was performed from April 2008 to August 2013 and whose postoperative corrected distance visual acuity (CDVA) was 20/40 or better in the operated eye. Eyes with traumatic cataracts, a history of ocular surgery, eventful surgery (eg, anterior capsule tear), or postoperative complications were excluded. Patients with a medical record of noticeable postoperative toric IOL rotation or decentration were also excluded. Institutional review board approval was obtained from Korea University Anam Hospital and Korea University Guro Hospital, Seoul, South Korea. All research and data collection adhered to the tenets of the Declaration of Helsinki. Informed written consent was obtained from all participants.
Patient Examination The preoperative keratometry, ACD, and AL were measured using partial coherence interferometry (PCI) (IOLMaster, version 5.02 or higher). The IOL power was calculated using the SRK/T and Haigis formulas. The A-constant used for the SRK/T formula was 118.7, and the a0, a1, and a2 constants used for the Haigis formula were 0.111, 0.249, and 0.179, respectively. The cylinder power and toric IOL axis were calculated using an online toric IOL calculator programA with an expected incision-induced astigmatism value of 0.50 D. Postoperative UDVA, CDVA, and objective refractive error and keratometry, obtained using an autorefractor/keratometer (RK-F1, Canon, Inc.), were measured at a visit that occurred between 3 weeks and 10 weeks postoperatively.
Surgical Technique The patient was placed in an upright position to correct for cyclotorsion and was instructed to fixate on a distant target. The corneal limbus was marked at the 3-, 6-, and 9-o’clock positions using a preoperative toric reference marker (AE2793S, ASICO LLC) after topical anesthesia with proparacaine hydrochloride 0.5% (Alcaine). All phacoemulsification and toric IOL implantations were performed by 1 of 3 experienced surgeons (S.J.S., Y.Y.K., H.M.K.) at 1 of 2 hospitals at our institute. After a 2.20 mm or 2.75 mm temporal clear corneal incision was made, a continuous curvilinear capsulorhexis slightly smaller than the IOL optic size was created using a 26-gauge needle. A standard phacoemulsification technique was used. Intraoperatively, the alignment axis was marked using an intraoperative toric axis marker II (AE-2794N, ASICO LLC). The toric IOL was inserted in the capsular bag using a Monarch II injector (Alcon Laboratories, Inc.). After the ophthalmic viscosurgical device was removed, the IOL was rotated to the final position and verified using the alignment axis marks.
Main Outcome Measures The target induced astigmatism vector (TIA) was defined as the corneal plane effective cylinder power of the toric IOL predicted by the SRK/T and Haigis formulas. The TIAs according to the ELP and keratometry were calculated using a refractive vergence formula,12,13 as follows: Dcornea Z
1336 K0 þ ELP
1336 þ DIOL
1336 1336ELP K0
where Dcornea is the corneal plane cylinder power of the toric IOL, K0 is the net corneal power, ELP is the effective lens position, and DIOL is the IOL plane cylinder power of the toric IOL. In the SRK/T formula,14,15 the ELP (the estimated postoperative ACD) was calculated as follows: The corneal radius of curvature: 337:5 K where r is the radius and K is the corneal power. rZ
The corrected AL (LCOR): If AL%24:2 then LCOR Z AL If ALO24:2 then LCOR Z 3:446 þ 1:716AL 0:0237AL2 where AL is the axial length and LCOR is the corrected AL. The computed corneal width (Cw ): Cw Z 5:40948 þ 0:58412LCOR þ 0:098K
Submitted: October 16, 2014. Final revision submitted: December 13, 2014. Accepted: December 17, 2014.
The corneal height (H): C2w 4 If x!0 then x Z 0 pffiffiffi HZr x x Z r2
From the Department of Ophthalmology, Korea University College of Medicine, Seoul, South Korea. Corresponding author: Hyo Myung Kim, MD, PhD, Department of Ophthalmology, Anam Hospital, Korea University College of Medicine, 126-1, Anam-dong 5-ga, Seongbuk-gu, Seoul, 136-705, South Korea. E-mail: [email protected].
Determining the ACD constant (ACDconst) from the A-constant:
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ACDconst Z 0:62467A 68:747 where A is the A-constant with the value 118.7. The offset for the IOL model to be implanted: Offset Z ACDconst 3:336 The estimated postoperative ACD: ACDest Z H þ Offset The regression equation used to predict postoperative ELP in the Haigis formula16 was: ELP Z a0 þ a1 ACD þ a2 AL where a0, a1, and a2 are constants with the values 0.111, 0.249, and 0.179, respectively. The surgically induced astigmatism (SIA) vector was defined as the vector of postoperatively achieved cylindrical correction by toric IOLs at visits between 3 weeks and 10 weeks postoperatively. Postoperative corneal astigmatism and postoperative corneal plane refractive astigmatism were used to calculate the SIA using the Alpins vectorial method.17,18 The magnitude (D) and axis (degree) of incision-induced corneal astigmatism change were calculated using the SIA calculator (Excel, version 2.1, Microsoft Corp.).11,B The median absolute magnitude of error was defined as the median absolute value of the magnitude of error. The magnitude of error was defined as the difference between the magnitudes of the SIA and the TIA. The median absolute error was defined as the median absolute value of the predicted refractive error. The predicted refractive error was defined as the difference between the objective refractive spherical equivalent (SE) measured at the postoperative examination and the preoperative refraction predicted by PCI using the SRK/T and Haigis formulas (the predicted refractive error equals the postoperative SE minus the preoperative predicted refraction). The dataadjusted A-constant for the SRK/T formula was calculated using the Haigis constant optimization Excel spreadsheet for optical biometry, which also optimizes an IOL constant for the SRK/T formula.19,C The data-adjusted a0, a1, and a2 constants for the Haigis formula were calculated with linear regression analysis from the back-calculated ELP (see below) to get a zero mean arithmetic error in IOL power prediction. The optimized predicted refractive error of the SRK/T and Haigis formulas based on the data-adjusted IOL constants was used to calculate median absolute errors. The back-calculated ELP was defined as the postoperatively estimated ELP based on preoperative K, the AL, the implanted IOL power, and the postoperative refractive error using a thin-lens formula20,21 as follows: IOLpower Z
n 1000 n 1000 AL ELP n Z1000 ELP
where ZZ
ðnc 1Þ1000 R þ rcornea 1 R dv
where n is the refractive index of aqueous and vitreous (1.336), AL is the axial length, ELP is the effective lens position, nc is the fictitious refractive index of cornea (1.3315), rcornea is the corneal radius of curvature, R is the postoperatively achieved refraction, and dv is vertex distance.
Investigation of the Theoretical Method of Predicting Corneal Plane Cylinder Power of Toric Intraocular Lenses To investigate the validity of the method of predicting the TIA by the SRK/T and Haigis formulas using a refractive vergence formula, the TIA was compared with the predicted corneal plane cylinder power of the toric IOLs using the AMOD and ZeissE online calculators. The AMO calculator uses the SRK/T formula, and the Zeiss calculator uses the Haigis formula. Keratometry values (range 40 D to 46 D), ACD (range 2.00 mm to 4.00 mm), and AL (range 21.0 mm to 27.0 mm) were used to calculate the TIA as predicted by the SRK/T and Haigis formulas using a refractive vergence formula. The A-constant was 119.3 when calculating the TIA with the SRK/T formula. In the Haigis formula, the ELP within the Zeiss calculator was used. The same range of values of K, ACD, and AL was entered into the online calculators to calculate the predicted corneal plane cylinder power of the toric IOL according to the AMO and Zeiss calculators. All values were entered into the right eye in the online calculators, and surgically induced corneal astigmatism was set to zero. In the AMO calculator, the IOL power was selected based on a predicted refraction of 0.5 to 0.0 D of the SRK/T formula with an A-constant of 119.3 using PCI. In the Zeiss calculator, the IOL power was selected based on a predicted refraction of 0.5 to 0.0 D. The results were expressed as the ratio of toricity, defined as the ratio between the cylinder power of the toric IOL at the IOL plane and the corresponding cylinder power at the corneal plane.10 The theoretically calculated ratio of toricity determined by the IOL formulas with a refractive vergence formula was compared to the ratio of toricity predicted by the online calculators.
Statistical Analysis Descriptive statistics for all patient data and theoretical analysis data were obtained using the Statistical Package for the Social Sciences (version 20.0, SPSS, Inc.). Wilcoxon signed-rank tests were performed to compare the median absolute magnitudes of error and median absolute errors predicted by the SRK/T and Haigis formulas. Paired t tests were performed to compare the magnitude of error, the TIA, and the mean absolute error predicted by the SRK/T and Haigis formulas. The paired t test with the Bonferroni correction was used for comparison of ELPs predicted by the SRK/T and Haigis formulas and the back-calculated ELP (P ! .017). Pearson correlation analyses were performed to evaluate the relationship between the back-calculated ELP and the ELP predicted by the SRK/T or Haigis formula. Linear regression analyses were performed to evaluate the relationship between the ratio of toricity predicted by the IOL formulas with a refractive vergence formula and that predicted by the online calculators. A P value less than 0.05 was considered statistically significant.
RESULTS The study evaluated 73 eyes of 73 patients, 28 (38.4%) men and 45 (61.6%) women. Table 1 shows other patient demographics and clinical characteristics as well as laterality and calculated IOL power and
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Table 1. Clinical characteristics of cataract patients (N Z 73). Parameter Age (y) Laterality Right eye Left eye Mean K (corneal power) (D) Corneal astigmatism (D) Anterior chamber depth (mm) Axial length (mm) Intraocular lens power (D) Intraocular lens cylinder power* (D)
Mean G SD
Range
62.4 G 13.4
23, 89
44.82 G 1.66 2.04 G 0.69 3.22 G 0.45 23.52 G 1.27 20.0 G 4.0 2.26 G 0.63
40.67, 48.87 0.96, 4.38 2.00, 3.99 21.06, 27.27 7.0, 29.0 1.50, 3.00
n (%)
37 (50.7) 36 (49.3) d d d d d d
*The cylinder power of the toric IOL at the IOL plane
cylinder power. Table 2 gives the data determined using the SRK/T and Haigis formulas for predicting the corneal astigmatism correction by the toric IOL. The mean postoperative corneal plane cylinder power of refractive error was 0.55 G 0.52 D. The magnitude and axis of incision-induced corneal astigmatism changes were 0.20 D at 92 degrees. The mean TIA predicted by the Haigis formula was statistically significantly greater than the mean TIA predicted by the SRK/T formula (P ! .001). The median absolute magnitude of error predicted by the Haigis formula was statistically significantly smaller than that predicted by the SRK/T formula (P ! .001). Table 3 gives the median absolute error and mean predicted refractive error determined by the SRK/T and Haigis formulas for IOL power calculation. The median absolute error predicted by the Haigis formula was statistically significantly smaller than that predicted by the SRK/T formula (P Z .003). After optimization of the predicted refractive error of the SRK/T and Haigis formulas, the median absolute error predicted by the Haigis formula was still statistically significantly smaller than that predicted by the SRK/T formula (P Z .001).
The mean back-calculated ELP was 4.97 G 0.38 mm. The mean postoperative ELP predicted by the SRK/T formula was 5.55 G 0.51 mm and by the Haigis formula was 4.90 G 0.29 mm. The mean ELP predicted by the SRK/T formula was statistically significantly larger than the mean back-calculated ELP (P ! .001, paired t test); however, there was no statistically significant difference between the back-calculated ELP and the ELP predicted by the Haigis formula (P Z .080, paired t test). A Pearson correlation analysis showed that the back-calculated ELP was positively correlated with the ELP predicted by the Haigis formula (r Z 0.445, P ! .001) but not with the ELP predicted by the SRK/T formula (r Z 0.158, P Z .183). Investigation of the Theoretical Method of Predicting Corneal Plane Cylinder Power of Toric Intraocular Lenses The ratio of toricity predicted by the SRK/T formula using a refractive vergence formula was strongly correlated with that predicted by the AMO calculator (R2 Z 0.985, P ! .001) (Figure 1, A). There was also a strong correlation between the ratio of toricity
Table 2. Data determined by the SRK/T and Haigis formulas for predicting corneal astigmatism correction by a toric IOL (N Z 73). Data (D) Median absolute magnitude of error* Mean magnitude of error† Mean TIA† Mean SIA†
SRK/T
Haigis
P Value
0.30 (0.12, 0.53) 0.31 G 0.40 1.49 G 0.41 1.80 G 0.55
0.30 (0.11, 0.45) 0.23 G 0.40 1.57 G 0.43 1.80 G 0.55
!.001z !.001x !.001x d
Magnitude of error Z the difference between the magnitudes of the SIA and the TIA; SIA Z surgically induced astigmatism vector; TIA Z target induced astigmatism vector *Given as median (interquartile range) † Given as mean G SD z Wilcoxon signed-rank test x Paired t test
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Table 3. Data determined by the SRK/T and Haigis formulas for toric IOL power calculation (N Z 73). Datum Median absolute error* (D) Mean absolute error† (D) Mean predicted refractive errorz (D) Patients achieved predicted refractive error, n (%) G0.25 D G0.50 D G1.00 D OG2.00 D Median absolute error (opt)* (D) Mean absolute error (opt)† (D) Mean predicted refractive error (opt){ (D) Patients achieved predicted refractive error (opt), n (%) G0.25 D G0.50 D G1.00 D OG2.00 D
SRK/T
Haigis
0.43 (0.26, 0.65) 0.48 G 0.32 0.06 (1.18, 1.30)
0.35 (0.15, 0.53) 0.36 G 0.25 0.13 (0.87, 1.10)
18 (24.7) 44 (60.3) 67 (91.8) 0 (0.0) 0.44 (0.21, 0.66) 0.47 G 0.31 0.00 (1.22, 1.18)
25 (34.2) 53 (72.6) 71 (97.3) 0 (0.0) 0.32 (0.13, 0.50) 0.33 G 0.24 0.00 (0.86, 0.83)
23 (31.5) 46 (63.0) 67 (91.8) 0 (0.0)
31 (42.5) 55 (75.3) 73 (100.0) 0 (0.0)
P Value .003† .001x
.001† !.001x
Opt Z calculated optimized values based on the data-adjusted intraocular lens constants *Given as median (interquartile range) † Wilcoxon signed-rank test z Given as mean G SD x Paired t test { Given as mean (range)
predicted by the Haigis formula using a refractive vergence formula and that predicted by the Zeiss calculator (R2 Z 0.991, P ! .001) (Figure 1, B). DISCUSSION This study showed that the Haigis formula was more accurate than the SRK/T formula in predicting corneal astigmatism correction by toric IOLs. Previous studies showed that the amount of corneal astigmatism correction by a toric IOL is affected by K, ACD, pachymetry, ELP, and AL values.9–11 Among those, the ELP is estimated differently for the IOL formulas. Thus, the accuracy of the IOL formulas in predicting corneal astigmatism correction by toric IOLs could vary, just as the accuracy of predicting refractive outcome varies among the IOL formulas.19,22 The SRK/T formula overestimates the ELP when the K value is steep and underestimates it when K is flat, whereas the Haigis formula does not.19 In fact in this study, the Haigis formula was more accurate than the SRK/T formula in predicting both refractive outcome and corneal astigmatism correction by toric IOLs. The more accurate IOL formula might more accurately predict the amount of corneal astigmatism correction by toric IOLs. The SRK/T and Haigis formulas both underestimated the amount of corneal astigmatism correction
by toric IOLs, although in this study, the Haigis formula was more accurate than the SRK/T formula. The back-calculated ELP was not different from the estimated ELP predicted by the Haigis formula but was statistically significantly smaller than that predicted by the SRK/T formula. A previous study11 showed that a deeper ELP resulted in a less efficacious toric IOL in terms of correction of corneal astigmatism. Thus, the SRK/T formula, whose ELP values were statistically significantly larger than the back-calculated ELP, might underestimate the amount of corneal astigmatism correction by a toric IOL. The Haigis formula also underestimated the amount of corneal astigmatism correction by a toric IOL, even though the TIA predicted by the Haigis formula was statistically significantly larger than that predicted by the SRK/T formula. Thus, it seems that the calculated method for predicting corneal astigmatism correction by a toric IOL using the IOL formulas and a refractive vergence formula should be optimized to achieve a zero magnitude of error for the entire dataset because optimizing IOL formula constants allows the predicted refractive error to be zero. The toric IOLs used in this study provide toricity on the posterior optic surface. Other toric IOLs provide toricity on the anterior optic surface or on the anterior and posterior optic surfaces of the IOL. Thus, the effective toric surface position might differ among IOL
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Figure 1. Comparison of the ratio of toricity predicted by the online toric IOL calculators with that predicted by theoretical analysis using the SRK/T and Haigis formulas with a refractive vergence formula. A: Comparison between the AMO calculator and the SRK/T formula with a refractive vergence formula. B: Comparison between the Zeiss calculator and the Haigis formula with a refractive vergence formula.
models, even though the ELP is the same. In addition, the effective toric surface position might vary according to IOL power because the central optic thickness of an IOL changes based on the IOL power. Thus, the effective toric surface position based on IOL surface design and IOL power should be considered when IOL formulas and refractive vergence are being optimized to a specific toric IOL to calculate the predicted corneal astigmatism correction. When we compared the theoretically calculated predictions of corneal astigmatism correction that were determined by the SRK/T and Haigis formulas using a refractive vergence formula for the prediction of corneal astigmatism correction according to the online toric IOL calculators, the ratios of toricity predicted by the SRK/T and Haigis formulas showed a strong correlation with those predicted by the AMO and Zeiss calculators, respectively. These results support the validity of predicting TIA using the SRK/T and Haigis formulas with a refractive vergence formula; however, these results also indirectly suggest that currently available online calculators are not entirely accurate and might have to be optimized for individual surgeons. One limitation of the present study is that the sample size was relatively small and the medical records were reviewed retrospectively. Another limitation is that it did not evaluate the amount of postoperative axis misalignment of toric IOLs. Axis misalignment
reduces the effectiveness of toric IOLs in correcting corneal astigmatism and results in increased residual astigmatism.23 However, this study compared the accuracy of the SRK/T and Haigis formulas for predicting corneal astigmatism correction by toric IOLs by comparing the SIA and the TIA, as predicted by the SRK/T and Haigis formulas. Thus, axis misalignment of toric IOLs might have a similar effect on the SRK/T and Haigis formulas for predicting corneal astigmatism correction. In this study, the SIA was larger than the TIA as predicted by both the SRK/T and the Haigis formulas, even though axis misalignment of toric IOLs reduces SIA. The study also excluded patients with medical records showing eyes with noticeable postoperative toric IOL rotation or decentration. A third limitation of this study is that it used objective refraction measured with an autorefractor/ keratometer for measuring the postoperative refractive outcome. We also used the postoperative corneal astigmatism value measured with the same instrument. Thus, the measurements of the postoperative corneal astigmatism and postoperative corneal plane refractive astigmatism were performed on the same axis and using the same reference for centration to calculate the SIA. Previous studies also showed that autorefractor measurements were not significantly different from subjective refraction.24–26 A fourth limitation is that corneal astigmatism was measured from the anterior corneal surface. Previous studies
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showed that ignoring posterior corneal astigmatism results in errors in the estimation of total corneal astigmatism.27,28 Thus, a large-scale prospective study that considers the axis alignment of toric IOLs and both anterior and posterior corneal astigmatism is needed to compare the accuracy of the IOL formulas and to improve the ability of the IOL formulas to predict corneal astigmatism correction by toric IOLs. In conclusion, the Haigis formula was more accurate than the SRK/T formula in predicting the refractive outcome and in predicting corneal astigmatism correction by toric IOLs. The prediction method of corneal astigmatism correction by toric IOLs using an IOL formula and a refractive vergence formula should be optimized to achieve a zero magnitude of error for each individual surgeon. WHAT WAS KNOWN The corneal astigmatism correction of toric IOLs is affected by not only the rotational stability of the toric IOL, but also by the pachymetry, K, ACD, AL, and ELP values. The SRK/T and Haigis formulas suggest different ELPs using their own methods. WHAT THIS PAPER ADDS The Haigis formula was more accurate than the SRK/T formula in predicting the refractive outcome and in predicting corneal astigmatism correction by toric IOLs.
REFERENCES 1. Rubenstein JB, Raciti M. Approaches to corneal astigmatism in cataract surgery. Curr Opin Ophthalmol 2013; 24:30–34 2. Mendicute J, Irigoyen C, Ruiz M, Illarramendi I, Ferrer-Blasco T, s-Mico R. Toric intraocular lens versus opposite clear Monte corneal incisions to correct astigmatism in eyes having cataract surgery. J Cataract Refract Surg 2009; 35:451–458 ~oz-Negrete FJ, Kim HRW, Morcillo-Laiz R, 3. Mingo-Botın D, Mun Rebolleda G, Oblanca N. Comparison of toric intraocular lenses and peripheral corneal relaxing incisions to treat astigmatism during cataract surgery. J Cataract Refract Surg 2010; 36:1700–1708 4. Eom Y, Nam KT, Kang SY, Kim HM, Song JS. Axis difference between corneal and internal astigmatism to consider for toric intraocular lenses. Am J Ophthalmol 2013; 156:1112–1119 5. Novis C. Astigmatism and toric intraocular lenses. Curr Opin Ophthalmol 2000; 11:47–50 6. Viestenz A, Seitz B, Langenbucher A. Evaluating the eye’s rotational stability during standard photography; effect on determining the axial orientation of toric intraocular lenses. J Cataract Refract Surg 2005; 31:557–561 € tzner A, Becker R, Pavlovic S. 7. Weinand F, Jung A, Stein A, Pfu Rotational stability of a single-piece hydrophobic acrylic intraocular lens: new method for high-precision rotation control. J Cataract Refract Surg 2007; 33:800–803
8. Eom Y, Kang SY, Song J-S, Kim HM. Comparison of the actual amount of axial movement of 3 aspheric intraocular lenses using anterior segment optical coherence tomography. J Cataract Refract Surg 2013; 39:1528–1533 9. Goggin M, Moore S, Esterman A. Outcome of toric intraocular lens implantation after adjusting for anterior chamber depth and intraocular lens sphere equivalent power effects. Arch Ophthalmol 2011; 129:998–1003. correction, 1494. Available at: http://archopht.jamanetwork.com/data/Journals/OPHTH/22540 /ecs05115_998_1003.pdf. Correction available at: http://archopht.jamanetwork.com/data/Journals/OPHTH/22547/ecx1501 1_1494_1494.pdf. Accessed June 11, 2015 10. Savini G, Hoffer KJ, Carbonelli M, Ducoli P, Barboni P. Influence of axial length and corneal power on the astigmatic power of toric intraocular lenses. J Cataract Refract Surg 2013; 39:1900–1903 11. Eom Y, Kang SY, Song JS, Kim YY, Kim HM. Effect of effective lens position on cylinder power of toric intraocular lenses. Can J Ophthalmol 2015; 50:26–32 12. Holladay JT. Refractive power calculations for intraocular lenses in the phakic eye. Am J Ophthalmol 1993; 116:63–66 13. Holladay JT. Standardizing constants for ultrasonic biometry, keratometry, and intraocular lens power calculations. J Cataract Refract Surg 1997; 23:1356–1370. Available at: http://www.docholladay.com/publications/StandardizingConst ants.pdf. Accessed June 11, 2015 14. Retzlaff JA, Sanders DR, Kraff MC. Development of the SRK/T intraocular lens implant power calculation formula. J Cataract Refract Surg 1990; 16:333–340; erratum, 528 15. Haigis W. Occurrence of erroneous anterior chamber depth in the SRK/T formula [letter]. J Cataract Refract Surg 1993; 19:442–443; reply by JA Retzlaff, DR Sanders, MC Kraff, 443– 446 16. Haigis W. The Haigis formula. In: Shammas HJ, ed, Intraocular Lens Power Calculations. Thorofare, NJ, Slack, 2004; 41–57 17. Alpins NA. A new method of analyzing vectors for changes in astigmatism. J Cataract Refract Surg 1993; 19:524–533 18. Alpins N. Astigmatism analysis by the Alpins method. J Cataract Refract Surg 2001; 27:31–49 19. Eom Y, Kang SY, Song J-S, Kim HM. Use of corneal powerspecific constants to improve the accuracy of the SRK/T formula. Ophthalmology 2013; 120:477–481 20. Colenbrander MC. Calculation of the power of an iris clip lens for distant vision. Br J Ophthalmol 1973; 57:735–740. Available at: http://www.pubmedcentral.nih.gov/picrender.fcgi?artidZ12151 53&blobtypeZpdf. Accessed June 11, 2015 21. Fyodorov SN, Galin MA, Linksz A. Calculation of the optical power of intraocular lenses. Invest Ophthalmol 1975; 14:625–628. Available at: http://iovs.arvojournals.org/article.aspx?articleidZ2175293. Accessed June 11, 2015 22. Eom Y, Kang S-Y, Song JS, Kim YY, Kim HM. Comparison of Hoffer Q and Haigis formulae for intraocular lens power calculation according to the anterior chamber depth in short eyes. Am J Ophthalmol 2014; 157:818–824 23. Tseng SS, Ma JJK. Calculating the optimal rotation of a misaligned toric intraocular lens. J Cataract Refract Surg 2008; 34:1767–1772 24. Raj PS, Akingbehin T, Levy AM. Objective autorefraction in posterior chamber pseudophakia. Br J Ophthalmol 1990; 74:731– 733. Available at: http://www.ncbi.nlm.nih.gov/pmc/articles/ PMC1042277/pdf/brjopthal00586-0030.pdf. Accessed June 11, 2015 25. Zadnik K, Mutti DO, Adams AJ. The repeatability of measurement of the ocular components. Invest Ophthalmol Vis Sci 1992; 33:2325–2333. Available at: http://iovs.arvojournals.org/ article.aspx?articleidZ2179254. Accessed June 11, 2015
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26. Rosenfield M, Chiu NN. Repeatability of subjective and objective refraction. Optom Vis Sci 1995; 72:77–579. Available at: http:// journals.lww.com/optvissci/Abstract/1995/08000/Repeatability _of_Subjective_and_Objective.7.aspx. Accessed June 11, 2015 27. Koch DD, Ali SF, Weikert MP, Shirayama M, Jenkins R, Wang L. Contribution of posterior corneal astigmatism to total corneal astigmatism. J Cataract Refract Surg 2012; 38:2080–2087 28. Eom Y, Kang SY, Kim HM, Song JS. The effect of posterior corneal flat meridian and astigmatism amount on the total corneal astigmatism estimated from anterior corneal measurements. Graefes Arch Clin Exp Ophthalmol 2014; 252:1769–1777
C. Hill W. IOL power calculations physician downloads. Haigis formula optimization. Available at: http://doctor-hill.com/physicians/download.htm. Accessed June 11, 2015 D. Abbott Medical Optics, Inc. AMO IOL calculator platform. Available at: www.TecnisToricCalc.com. Accessed June 11, 2015 E. Carl Zeiss Meditec AG. [Online calculator] Available at: https://zcalc.meditec.zeiss.com/zcalc/. Accessed June 11, 2015
OTHER CITED MATERIAL
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A. Alcon, Inc. AcrySof Toric IOL Web Based Calculators. Available at: http://www.acrysoftoriccalculator.com. Accessed June 11, 2015 B. Sawhney S, Aggarwal A. Insight eye clinic. SIA Calculator v 2.1. Available at: http://www.insighteyeclinic.in/download/SIA_ Calc_v_2.1.xlsx. Accessed June 11, 2015
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First author: Youngsub Eom, MD Department of Ophthalmology, Korea University College of Medicine, Seoul, South Korea
Comparison of SRK/T and Haigis formulas for predicting corneal astigmatism correction with toric intraocular lenses Youngsub Eom, MD, Jong Suk Song, MD, PhD, Yong Yeon Kim, MD, PhD, Hyo Myung Kim, MD, PhD
PURPOSE: To compare the accuracy of the SRK/T and Haigis formulas for predicting corneal astigmatism correction with a toric intraocular lens (IOL). SETTING: Department of Ophthalmology, Korea University College of Medicine, Seoul, South Korea. DESIGN: Retrospective cross-sectional study. METHODS: Eyes with an Acrysof toric IOL were enrolled in the study. The corneal plane effective cylinder power of toric IOLs (target induced astigmatism vector [TIA]) predicted by the SRK/T and Haigis formulas were compared with the cylindrical correction achieved postoperatively (surgically induced astigmatism vector [SIA]). The magnitude of error was defined as the difference between the magnitudes of the SIA and TIA. The median absolute magnitudes of error predicted by the SRK/T and Haigis formulas were compared. The median absolute errors predicted by the 2 formulas were also compared. RESULTS: The mean postoperative SIA was 1.80 diopters (D) G 0.55 (SD). The magnitude of error predicted by the SRK/T and Haigis formulas was 0.31 G 0.40 D and 0.23 G 0.40 D, respectively. The median absolute magnitude of error predicted by the Haigis formula was statistically significantly smaller than that predicted by the SRK/T formula (P < .001). The median absolute error predicted by the Haigis formula (0.35 D) was also statistically significantly smaller than that predicted by the SRK/T formula (0.43 D) (P Z .003). CONCLUSION: The Haigis formula was more accurate than the SRK/T formula not only in predicting the refractive outcome but also in predicting corneal astigmatism correction by toric IOLs. Financial Disclosure: No author has a financial or proprietary interest in any material or method mentioned. J Cataract Refract Surg 2015; 41:1650–1657 Q 2015 ASCRS and ESCRS
Corneal astigmatism is a cause of reduced uncorrected distance visual acuity (UDVA) after cataract surgery.1 Corneal astigmatism can be reduced using a toric intraocular lenses (IOLs), which are effective and perform well in predicting corneal astigmatism correction.2,3 When using toric IOLs, it is important to select patients who are good candidates4 and to be precise when predicting the corneal astigmatism correction. Rotational stability has been the primary focus of many previous studies evaluating toric IOL outcomes5–7; however, because IOL refractive outcomes are affected by the postoperative effective lens position (ELP),8 the corneal plane effective cylinder power of toric IOLs might also be affected by the postoperative 1650
Q 2015 ASCRS and ESCRS Published by Elsevier Inc.
position. Goggin et al.9 showed that anterior chamber depth (ACD) and pachymetry also affect corneal astigmatism correction by toric IOLs. Savini et al.10 showed that the corneal plane theoretical toricity of toric IOLs varies according to the corneal power (keratometry [K]), ACD, and axial length (AL). Another previous study11 showed that the corneal plane effective cylinder power of toric IOLs was affected by the ELP. Currently, several types of toric IOLs are commercially available with their own online toric IOL calculators. Our institute has used 3 toric IOLs: Acrysof toric (Alcon Laboratories, Inc.), Tecnis toric (Abbott Medical Optics, Inc.), and Zeiss toric (Carl Zeiss Meditec AG). To determine toric IOL cylinder power, the
http://dx.doi.org/10.1016/j.jcrs.2014.12.053 0886-3350
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Abbott Medical Optics (AMO) calculator offers several modes, including the SRK/T formula. The Zeiss calculator provides toric IOL cylinder power based on the Haigis formula. The SRK/T and Haigis formulas suggest different ELPs, using their own methods. Because the corneal plane effective cylinder power of toric IOLs is affected by the ELP,11 the accuracy of prediction of corneal astigmatism correction by toric IOLs might be different between the IOL formulas. This study compared the accuracies of the SRK/T and Haigis formulas for predicting corneal astigmatism correction by toric IOLs. PATIENTS AND METHODS Study Population This retrospective study included eyes in which uneventful phacoemulsification with implantation of an Acrysof SN60T3-T5 (Alcon Laboratories, Inc.) toric IOL 1.50 to 3.00 diopters (D) cylinder was performed from April 2008 to August 2013 and whose postoperative corrected distance visual acuity (CDVA) was 20/40 or better in the operated eye. Eyes with traumatic cataracts, a history of ocular surgery, eventful surgery (eg, anterior capsule tear), or postoperative complications were excluded. Patients with a medical record of noticeable postoperative toric IOL rotation or decentration were also excluded. Institutional review board approval was obtained from Korea University Anam Hospital and Korea University Guro Hospital, Seoul, South Korea. All research and data collection adhered to the tenets of the Declaration of Helsinki. Informed written consent was obtained from all participants.
Patient Examination The preoperative keratometry, ACD, and AL were measured using partial coherence interferometry (PCI) (IOLMaster, version 5.02 or higher). The IOL power was calculated using the SRK/T and Haigis formulas. The A-constant used for the SRK/T formula was 118.7, and the a0, a1, and a2 constants used for the Haigis formula were 0.111, 0.249, and 0.179, respectively. The cylinder power and toric IOL axis were calculated using an online toric IOL calculator programA with an expected incision-induced astigmatism value of 0.50 D. Postoperative UDVA, CDVA, and objective refractive error and keratometry, obtained using an autorefractor/keratometer (RK-F1, Canon, Inc.), were measured at a visit that occurred between 3 weeks and 10 weeks postoperatively.
Surgical Technique The patient was placed in an upright position to correct for cyclotorsion and was instructed to fixate on a distant target. The corneal limbus was marked at the 3-, 6-, and 9-o’clock positions using a preoperative toric reference marker (AE2793S, ASICO LLC) after topical anesthesia with proparacaine hydrochloride 0.5% (Alcaine). All phacoemulsification and toric IOL implantations were performed by 1 of 3 experienced surgeons (S.J.S., Y.Y.K., H.M.K.) at 1 of 2 hospitals at our institute. After a 2.20 mm or 2.75 mm temporal clear corneal incision was made, a continuous curvilinear capsulorhexis slightly smaller than the IOL optic size was created using a 26-gauge needle. A standard phacoemulsification technique was used. Intraoperatively, the alignment axis was marked using an intraoperative toric axis marker II (AE-2794N, ASICO LLC). The toric IOL was inserted in the capsular bag using a Monarch II injector (Alcon Laboratories, Inc.). After the ophthalmic viscosurgical device was removed, the IOL was rotated to the final position and verified using the alignment axis marks.
Main Outcome Measures The target induced astigmatism vector (TIA) was defined as the corneal plane effective cylinder power of the toric IOL predicted by the SRK/T and Haigis formulas. The TIAs according to the ELP and keratometry were calculated using a refractive vergence formula,12,13 as follows: Dcornea Z
1336 K0 þ ELP
1336 þ DIOL
1336 1336ELP K0
where Dcornea is the corneal plane cylinder power of the toric IOL, K0 is the net corneal power, ELP is the effective lens position, and DIOL is the IOL plane cylinder power of the toric IOL. In the SRK/T formula,14,15 the ELP (the estimated postoperative ACD) was calculated as follows: The corneal radius of curvature: 337:5 K where r is the radius and K is the corneal power. rZ
The corrected AL (LCOR): If AL%24:2 then LCOR Z AL If ALO24:2 then LCOR Z 3:446 þ 1:716AL 0:0237AL2 where AL is the axial length and LCOR is the corrected AL. The computed corneal width (Cw ): Cw Z 5:40948 þ 0:58412LCOR þ 0:098K
Submitted: October 16, 2014. Final revision submitted: December 13, 2014. Accepted: December 17, 2014.
The corneal height (H): C2w 4 If x!0 then x Z 0 pffiffiffi HZr x x Z r2
From the Department of Ophthalmology, Korea University College of Medicine, Seoul, South Korea. Corresponding author: Hyo Myung Kim, MD, PhD, Department of Ophthalmology, Anam Hospital, Korea University College of Medicine, 126-1, Anam-dong 5-ga, Seongbuk-gu, Seoul, 136-705, South Korea. E-mail: [email protected].
Determining the ACD constant (ACDconst) from the A-constant:
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ACDconst Z 0:62467A 68:747 where A is the A-constant with the value 118.7. The offset for the IOL model to be implanted: Offset Z ACDconst 3:336 The estimated postoperative ACD: ACDest Z H þ Offset The regression equation used to predict postoperative ELP in the Haigis formula16 was: ELP Z a0 þ a1 ACD þ a2 AL where a0, a1, and a2 are constants with the values 0.111, 0.249, and 0.179, respectively. The surgically induced astigmatism (SIA) vector was defined as the vector of postoperatively achieved cylindrical correction by toric IOLs at visits between 3 weeks and 10 weeks postoperatively. Postoperative corneal astigmatism and postoperative corneal plane refractive astigmatism were used to calculate the SIA using the Alpins vectorial method.17,18 The magnitude (D) and axis (degree) of incision-induced corneal astigmatism change were calculated using the SIA calculator (Excel, version 2.1, Microsoft Corp.).11,B The median absolute magnitude of error was defined as the median absolute value of the magnitude of error. The magnitude of error was defined as the difference between the magnitudes of the SIA and the TIA. The median absolute error was defined as the median absolute value of the predicted refractive error. The predicted refractive error was defined as the difference between the objective refractive spherical equivalent (SE) measured at the postoperative examination and the preoperative refraction predicted by PCI using the SRK/T and Haigis formulas (the predicted refractive error equals the postoperative SE minus the preoperative predicted refraction). The dataadjusted A-constant for the SRK/T formula was calculated using the Haigis constant optimization Excel spreadsheet for optical biometry, which also optimizes an IOL constant for the SRK/T formula.19,C The data-adjusted a0, a1, and a2 constants for the Haigis formula were calculated with linear regression analysis from the back-calculated ELP (see below) to get a zero mean arithmetic error in IOL power prediction. The optimized predicted refractive error of the SRK/T and Haigis formulas based on the data-adjusted IOL constants was used to calculate median absolute errors. The back-calculated ELP was defined as the postoperatively estimated ELP based on preoperative K, the AL, the implanted IOL power, and the postoperative refractive error using a thin-lens formula20,21 as follows: IOLpower Z
n 1000 n 1000 AL ELP n Z1000 ELP
where ZZ
ðnc 1Þ1000 R þ rcornea 1 R dv
where n is the refractive index of aqueous and vitreous (1.336), AL is the axial length, ELP is the effective lens position, nc is the fictitious refractive index of cornea (1.3315), rcornea is the corneal radius of curvature, R is the postoperatively achieved refraction, and dv is vertex distance.
Investigation of the Theoretical Method of Predicting Corneal Plane Cylinder Power of Toric Intraocular Lenses To investigate the validity of the method of predicting the TIA by the SRK/T and Haigis formulas using a refractive vergence formula, the TIA was compared with the predicted corneal plane cylinder power of the toric IOLs using the AMOD and ZeissE online calculators. The AMO calculator uses the SRK/T formula, and the Zeiss calculator uses the Haigis formula. Keratometry values (range 40 D to 46 D), ACD (range 2.00 mm to 4.00 mm), and AL (range 21.0 mm to 27.0 mm) were used to calculate the TIA as predicted by the SRK/T and Haigis formulas using a refractive vergence formula. The A-constant was 119.3 when calculating the TIA with the SRK/T formula. In the Haigis formula, the ELP within the Zeiss calculator was used. The same range of values of K, ACD, and AL was entered into the online calculators to calculate the predicted corneal plane cylinder power of the toric IOL according to the AMO and Zeiss calculators. All values were entered into the right eye in the online calculators, and surgically induced corneal astigmatism was set to zero. In the AMO calculator, the IOL power was selected based on a predicted refraction of 0.5 to 0.0 D of the SRK/T formula with an A-constant of 119.3 using PCI. In the Zeiss calculator, the IOL power was selected based on a predicted refraction of 0.5 to 0.0 D. The results were expressed as the ratio of toricity, defined as the ratio between the cylinder power of the toric IOL at the IOL plane and the corresponding cylinder power at the corneal plane.10 The theoretically calculated ratio of toricity determined by the IOL formulas with a refractive vergence formula was compared to the ratio of toricity predicted by the online calculators.
Statistical Analysis Descriptive statistics for all patient data and theoretical analysis data were obtained using the Statistical Package for the Social Sciences (version 20.0, SPSS, Inc.). Wilcoxon signed-rank tests were performed to compare the median absolute magnitudes of error and median absolute errors predicted by the SRK/T and Haigis formulas. Paired t tests were performed to compare the magnitude of error, the TIA, and the mean absolute error predicted by the SRK/T and Haigis formulas. The paired t test with the Bonferroni correction was used for comparison of ELPs predicted by the SRK/T and Haigis formulas and the back-calculated ELP (P ! .017). Pearson correlation analyses were performed to evaluate the relationship between the back-calculated ELP and the ELP predicted by the SRK/T or Haigis formula. Linear regression analyses were performed to evaluate the relationship between the ratio of toricity predicted by the IOL formulas with a refractive vergence formula and that predicted by the online calculators. A P value less than 0.05 was considered statistically significant.
RESULTS The study evaluated 73 eyes of 73 patients, 28 (38.4%) men and 45 (61.6%) women. Table 1 shows other patient demographics and clinical characteristics as well as laterality and calculated IOL power and
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Table 1. Clinical characteristics of cataract patients (N Z 73). Parameter Age (y) Laterality Right eye Left eye Mean K (corneal power) (D) Corneal astigmatism (D) Anterior chamber depth (mm) Axial length (mm) Intraocular lens power (D) Intraocular lens cylinder power* (D)
Mean G SD
Range
62.4 G 13.4
23, 89
44.82 G 1.66 2.04 G 0.69 3.22 G 0.45 23.52 G 1.27 20.0 G 4.0 2.26 G 0.63
40.67, 48.87 0.96, 4.38 2.00, 3.99 21.06, 27.27 7.0, 29.0 1.50, 3.00
n (%)
37 (50.7) 36 (49.3) d d d d d d
*The cylinder power of the toric IOL at the IOL plane
cylinder power. Table 2 gives the data determined using the SRK/T and Haigis formulas for predicting the corneal astigmatism correction by the toric IOL. The mean postoperative corneal plane cylinder power of refractive error was 0.55 G 0.52 D. The magnitude and axis of incision-induced corneal astigmatism changes were 0.20 D at 92 degrees. The mean TIA predicted by the Haigis formula was statistically significantly greater than the mean TIA predicted by the SRK/T formula (P ! .001). The median absolute magnitude of error predicted by the Haigis formula was statistically significantly smaller than that predicted by the SRK/T formula (P ! .001). Table 3 gives the median absolute error and mean predicted refractive error determined by the SRK/T and Haigis formulas for IOL power calculation. The median absolute error predicted by the Haigis formula was statistically significantly smaller than that predicted by the SRK/T formula (P Z .003). After optimization of the predicted refractive error of the SRK/T and Haigis formulas, the median absolute error predicted by the Haigis formula was still statistically significantly smaller than that predicted by the SRK/T formula (P Z .001).
The mean back-calculated ELP was 4.97 G 0.38 mm. The mean postoperative ELP predicted by the SRK/T formula was 5.55 G 0.51 mm and by the Haigis formula was 4.90 G 0.29 mm. The mean ELP predicted by the SRK/T formula was statistically significantly larger than the mean back-calculated ELP (P ! .001, paired t test); however, there was no statistically significant difference between the back-calculated ELP and the ELP predicted by the Haigis formula (P Z .080, paired t test). A Pearson correlation analysis showed that the back-calculated ELP was positively correlated with the ELP predicted by the Haigis formula (r Z 0.445, P ! .001) but not with the ELP predicted by the SRK/T formula (r Z 0.158, P Z .183). Investigation of the Theoretical Method of Predicting Corneal Plane Cylinder Power of Toric Intraocular Lenses The ratio of toricity predicted by the SRK/T formula using a refractive vergence formula was strongly correlated with that predicted by the AMO calculator (R2 Z 0.985, P ! .001) (Figure 1, A). There was also a strong correlation between the ratio of toricity
Table 2. Data determined by the SRK/T and Haigis formulas for predicting corneal astigmatism correction by a toric IOL (N Z 73). Data (D) Median absolute magnitude of error* Mean magnitude of error† Mean TIA† Mean SIA†
SRK/T
Haigis
P Value
0.30 (0.12, 0.53) 0.31 G 0.40 1.49 G 0.41 1.80 G 0.55
0.30 (0.11, 0.45) 0.23 G 0.40 1.57 G 0.43 1.80 G 0.55
!.001z !.001x !.001x d
Magnitude of error Z the difference between the magnitudes of the SIA and the TIA; SIA Z surgically induced astigmatism vector; TIA Z target induced astigmatism vector *Given as median (interquartile range) † Given as mean G SD z Wilcoxon signed-rank test x Paired t test
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Table 3. Data determined by the SRK/T and Haigis formulas for toric IOL power calculation (N Z 73). Datum Median absolute error* (D) Mean absolute error† (D) Mean predicted refractive errorz (D) Patients achieved predicted refractive error, n (%) G0.25 D G0.50 D G1.00 D OG2.00 D Median absolute error (opt)* (D) Mean absolute error (opt)† (D) Mean predicted refractive error (opt){ (D) Patients achieved predicted refractive error (opt), n (%) G0.25 D G0.50 D G1.00 D OG2.00 D
SRK/T
Haigis
0.43 (0.26, 0.65) 0.48 G 0.32 0.06 (1.18, 1.30)
0.35 (0.15, 0.53) 0.36 G 0.25 0.13 (0.87, 1.10)
18 (24.7) 44 (60.3) 67 (91.8) 0 (0.0) 0.44 (0.21, 0.66) 0.47 G 0.31 0.00 (1.22, 1.18)
25 (34.2) 53 (72.6) 71 (97.3) 0 (0.0) 0.32 (0.13, 0.50) 0.33 G 0.24 0.00 (0.86, 0.83)
23 (31.5) 46 (63.0) 67 (91.8) 0 (0.0)
31 (42.5) 55 (75.3) 73 (100.0) 0 (0.0)
P Value .003† .001x
.001† !.001x
Opt Z calculated optimized values based on the data-adjusted intraocular lens constants *Given as median (interquartile range) † Wilcoxon signed-rank test z Given as mean G SD x Paired t test { Given as mean (range)
predicted by the Haigis formula using a refractive vergence formula and that predicted by the Zeiss calculator (R2 Z 0.991, P ! .001) (Figure 1, B). DISCUSSION This study showed that the Haigis formula was more accurate than the SRK/T formula in predicting corneal astigmatism correction by toric IOLs. Previous studies showed that the amount of corneal astigmatism correction by a toric IOL is affected by K, ACD, pachymetry, ELP, and AL values.9–11 Among those, the ELP is estimated differently for the IOL formulas. Thus, the accuracy of the IOL formulas in predicting corneal astigmatism correction by toric IOLs could vary, just as the accuracy of predicting refractive outcome varies among the IOL formulas.19,22 The SRK/T formula overestimates the ELP when the K value is steep and underestimates it when K is flat, whereas the Haigis formula does not.19 In fact in this study, the Haigis formula was more accurate than the SRK/T formula in predicting both refractive outcome and corneal astigmatism correction by toric IOLs. The more accurate IOL formula might more accurately predict the amount of corneal astigmatism correction by toric IOLs. The SRK/T and Haigis formulas both underestimated the amount of corneal astigmatism correction
by toric IOLs, although in this study, the Haigis formula was more accurate than the SRK/T formula. The back-calculated ELP was not different from the estimated ELP predicted by the Haigis formula but was statistically significantly smaller than that predicted by the SRK/T formula. A previous study11 showed that a deeper ELP resulted in a less efficacious toric IOL in terms of correction of corneal astigmatism. Thus, the SRK/T formula, whose ELP values were statistically significantly larger than the back-calculated ELP, might underestimate the amount of corneal astigmatism correction by a toric IOL. The Haigis formula also underestimated the amount of corneal astigmatism correction by a toric IOL, even though the TIA predicted by the Haigis formula was statistically significantly larger than that predicted by the SRK/T formula. Thus, it seems that the calculated method for predicting corneal astigmatism correction by a toric IOL using the IOL formulas and a refractive vergence formula should be optimized to achieve a zero magnitude of error for the entire dataset because optimizing IOL formula constants allows the predicted refractive error to be zero. The toric IOLs used in this study provide toricity on the posterior optic surface. Other toric IOLs provide toricity on the anterior optic surface or on the anterior and posterior optic surfaces of the IOL. Thus, the effective toric surface position might differ among IOL
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Figure 1. Comparison of the ratio of toricity predicted by the online toric IOL calculators with that predicted by theoretical analysis using the SRK/T and Haigis formulas with a refractive vergence formula. A: Comparison between the AMO calculator and the SRK/T formula with a refractive vergence formula. B: Comparison between the Zeiss calculator and the Haigis formula with a refractive vergence formula.
models, even though the ELP is the same. In addition, the effective toric surface position might vary according to IOL power because the central optic thickness of an IOL changes based on the IOL power. Thus, the effective toric surface position based on IOL surface design and IOL power should be considered when IOL formulas and refractive vergence are being optimized to a specific toric IOL to calculate the predicted corneal astigmatism correction. When we compared the theoretically calculated predictions of corneal astigmatism correction that were determined by the SRK/T and Haigis formulas using a refractive vergence formula for the prediction of corneal astigmatism correction according to the online toric IOL calculators, the ratios of toricity predicted by the SRK/T and Haigis formulas showed a strong correlation with those predicted by the AMO and Zeiss calculators, respectively. These results support the validity of predicting TIA using the SRK/T and Haigis formulas with a refractive vergence formula; however, these results also indirectly suggest that currently available online calculators are not entirely accurate and might have to be optimized for individual surgeons. One limitation of the present study is that the sample size was relatively small and the medical records were reviewed retrospectively. Another limitation is that it did not evaluate the amount of postoperative axis misalignment of toric IOLs. Axis misalignment
reduces the effectiveness of toric IOLs in correcting corneal astigmatism and results in increased residual astigmatism.23 However, this study compared the accuracy of the SRK/T and Haigis formulas for predicting corneal astigmatism correction by toric IOLs by comparing the SIA and the TIA, as predicted by the SRK/T and Haigis formulas. Thus, axis misalignment of toric IOLs might have a similar effect on the SRK/T and Haigis formulas for predicting corneal astigmatism correction. In this study, the SIA was larger than the TIA as predicted by both the SRK/T and the Haigis formulas, even though axis misalignment of toric IOLs reduces SIA. The study also excluded patients with medical records showing eyes with noticeable postoperative toric IOL rotation or decentration. A third limitation of this study is that it used objective refraction measured with an autorefractor/ keratometer for measuring the postoperative refractive outcome. We also used the postoperative corneal astigmatism value measured with the same instrument. Thus, the measurements of the postoperative corneal astigmatism and postoperative corneal plane refractive astigmatism were performed on the same axis and using the same reference for centration to calculate the SIA. Previous studies also showed that autorefractor measurements were not significantly different from subjective refraction.24–26 A fourth limitation is that corneal astigmatism was measured from the anterior corneal surface. Previous studies
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showed that ignoring posterior corneal astigmatism results in errors in the estimation of total corneal astigmatism.27,28 Thus, a large-scale prospective study that considers the axis alignment of toric IOLs and both anterior and posterior corneal astigmatism is needed to compare the accuracy of the IOL formulas and to improve the ability of the IOL formulas to predict corneal astigmatism correction by toric IOLs. In conclusion, the Haigis formula was more accurate than the SRK/T formula in predicting the refractive outcome and in predicting corneal astigmatism correction by toric IOLs. The prediction method of corneal astigmatism correction by toric IOLs using an IOL formula and a refractive vergence formula should be optimized to achieve a zero magnitude of error for each individual surgeon. WHAT WAS KNOWN The corneal astigmatism correction of toric IOLs is affected by not only the rotational stability of the toric IOL, but also by the pachymetry, K, ACD, AL, and ELP values. The SRK/T and Haigis formulas suggest different ELPs using their own methods. WHAT THIS PAPER ADDS The Haigis formula was more accurate than the SRK/T formula in predicting the refractive outcome and in predicting corneal astigmatism correction by toric IOLs.
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First author: Youngsub Eom, MD Department of Ophthalmology, Korea University College of Medicine, Seoul, South Korea