Although toric intraocular lenses (IOLs) have improved the refractive outcomes of patients with significant preexisting astigmatism who have cataract surgery,1–4 the residual astigmatism is not always predictable.3,5 The underlying reasons for this are a matter of some controversy. Intraocular lens tilt, IOL rotational misalignment,6 and unexpected surgically induced astigmatism (SIA)2,7 all contribute to prediction errors; however, correcting for these factors does not always explain the postoperative astigmatic outcome.4,8
Accurate correction of astigmatism requires accurate measurements. Manual keratometry has been advocated as the preferred method to measure corneal astigmatism for the determination of the correct axis and cylinder power required for a toric IOL.9 Results in recent studies4,10,11 suggest that several devices are equivalent to manual keratometry. Other studies, however, emphasize the importance of net corneal astigmatic power, which is not available from standard keratometry and topography devices that are based on anterior corneal measurement.12,13 This issue was highlighted in 2012 by Koch,A who emphasized the role of the posterior cornea in assessing net corneal astigmatism in toric IOL calculations. In addition, successful correction of preexisting astigmatism requires accurate calculation of the required toric IOL cylinder power and axis of alignment. The toric online calculator by AlconB uses a fixed ratio to calculate the estimated IOL toric power at the corneal plane. In contrast, the Holladay toric calculatorC uses the predicted effective lens position (ELP) to determine the toric IOL power at the corneal plane. Neither of these calculators has internal adjustment to accommodate posterior corneal astigmatism when used with data provided by keratometers based on measurements of the anterior corneal curvature. The Baylor toric nomogram, which was described by Koch at el.,8 addresses this issue by taking into account the effect of the posterior cornea in the presence of with-the-rule (WTR) and against-the-rule (ATR) corneal astigmatism, and it can be used in conjunction with standard toric IOL calculators. The Barrett toric calculatorD uses the ELP of the Barrett Universal II formula14,E together with a mathematic model for the posterior cornea to calculate the required cylinder power and axis of a toric IOL.
In this study, we retrospectively evaluated a cohort of patients and examined 2 factors we thought might contribute to unexpected outcomes with toric IOLs; that is, the method of measuring corneal astigmatism and the method of predicting the required power and axis of a toric IOL. We excluded the influence of SIA and minimized errors in toric IOL alignment by using the postoperative corneal measurements and by measuring the actual toric IOL axis alignment. The purpose of our study was to compare the error in predicted residual astigmatism for different corneal measuring devices and several methods of calculation.
Patients and methods
This study reviewed the case records of consecutive patients who had cataract extraction with implantation of a toric Acrysof IOL (models SN6AT3 to SN6AT9, Alcon Laboratories, Inc.) through a 2.4 mm clear corneal incision by multiple surgeons at Ein-Tal Ophthalmology Center (private practice in Tel-Aviv, Israel) from February 2011 to September 2012. The study conformed to the Declaration of Helsinki and was approved by the Institutional Ethics Committee, Meir Medical Center, Kfar Saba, Israel.
Inclusion criteria were uneventful cataract surgery; postoperative manifest refraction at least 1 month after surgery with a corrected distance visual acuity of 20/30 or better; postoperative measurements at least 1 month after surgery (same day as the manifest refraction) with all 3 devices (partial coherence interferometry (PCI)–based IOLMaster 500, Carl Zeiss Meditec AG; optical low-coherence reflectometry (OLCR)–based Lenstar LS 900, Haag-Streit AG; Placido disk–based Atlas corneal topographer, Carl Zeiss Meditec AG), compatible with strict validation criteria by HillF; and postoperative toric IOL axis alignment measured by slitlamp and photography. All measurements were recorded at the same postoperative visit. The exclusion criteria were previous ocular trauma or surgery, intraoperative or postoperative complications, contact lens wear, and postoperative toric IOL decentration or tilt on slitlamp examination.
Three devices were used to measure corneal keratometry (K) values. The autokeratometry feature of the PCI device uses 6 light reflections projected off the anterior cornea at a diameter of 2.5 mm, depending on the corneal curvature. The validation criteria were a difference of 0.25 D or less between the 3 readings for the steep and flat K readings using 3 consecutive measurements. The dual-zone autokeratometry feature of the OLCR device uses 32 light reflections projected off the anterior cornea; the reflections are arranged in 2 concentric rings of 16 measuring points each. The outer ring has a diameter of 2.3 mm, and the inner ring has a diameter of 1.65 mm, depending on the corneal curvature. Each displayed K measurement is a composite of the mean of 4 measurements, totaling 128 measuring points. The validation criteria were a standard deviation (SD) less than 0.20 diopter (D) for the steep K and flat K and an SD less than 3.5 degrees for the axis of 5 consecutive measurements. The corneal topographer is a Placido disk–based device that provides simulated K values along the steepest and flattest meridians at the 3.0 mm annular zone and the mean K average values, which are calculated from all measured points within the central 3.0 mm zone. The validation criteria were an SD less than 0.20 D for the steep and flat Ks of 4 consecutive measurements.
Methods of Calculation
The online toric calculator by AlconB and the Holladay toric calculator were evaluated without and with the Baylor toric IOL nomogram adjustment.8 The online Barrett toric calculatorD was evaluated without adjustment.
Evaluation of the Error in Predicted Residual Astigmatism
Astigmatism values were calculated by subtracting the flat K values from the steep K values.
The assumed toric IOL cylinder power at the corneal plane was derived as follows: For the Alcon toric calculator, the toric IOL cylinder power was converted to the corneal plane using a fixed ratio as recommended on the Alcon toric calculator website.C For the Barrett toric calculator, the value was taken directly from the calculator printout.D For the Holladay toric calculator, the assumed toric IOL cylinder power at the corneal plane was indirectly calculated from the calculator printout by subtracting the predicted residual astigmatism from the predicted postoperative corneal astigmatism. To achieve optimum accuracy, the postoperative measured toric IOL alignment was used rather than the planned toric IOL alignment. The predicted residual astigmatism at the corneal plane was calculated by the sum of the assumed toric IOL cylinder power at the corneal plane and the measured corneal astigmatism taken by each device with or without adjustments for the Baylor nomogram.8 The error in the predicted residual astigmatism was calculated by subtracting the predicted residual astigmatism at the corneal plane from the postoperative subjective refraction at the corneal plane. The predicted residual astigmatism at the corneal plane was calculated by the sum of the assumed toric IOL cylinder power at the corneal plane and the measured corneal astigmatism taken by each device with or without adjustments for the Baylor nomogram. The error in predicted residual astigmatism was calculated by subtracting the predicted residual astigmatism at the corneal plane from the postoperative subjective refraction at the corneal plane. Vector analysis was used in all calculations.15 The Baylor nomogram for the adjustment of toric IOL power to account for posterior corneal astigmatism is based on regression analysis.8 The predicted net corneal astigmatism assessment for the Baylor nomogram was calculated using the published regression equations by subtracting (0.1005 × measured corneal astigmatism + 0.221) or adding (−0.011 × measured corneal astigmatism + 0.225) to the corneal astigmatism as measured by keratometry for WTR and ATR astigmatism, respectively.8,12 The mean absolute error, median absolute error, and centroid error in predicted residual astigmatism were calculated for each device and method. A subset analysis was performed by dividing the eyes into 2 groups depending on the anterior corneal steep meridian measured by the OLCR device as follows: (1) the WTR group, which had a corneal steep meridian at 60 to 120 degrees, and (2) the ATR group, which had a corneal steep meridian at 0 to 30 degrees or at 150 to 180 degrees. The centroid error in predicted residual astigmatism was then calculated using the OLCR device measurements for all methods of calculation.
A sample-size calculation was performed to detect an astigmatic prediction error of more than 0.20 D and an SD of 0.40 D. Thirty-four eyes were required for a significance level (α) of 0.05 and a test power of 0.80. Comparisons were performed for astigmatic predicted errors, including the x-axis and y-axis components for each device and calculation method. Data were checked for normality using the Shapiro-Wilks and Kolmogorov-Smirnov tests. The paired t test or the Wilcoxon nonparametric test was used as appropriate. The Fisher F test was used for comparisons of variants. A Bonferroni correction was used for multiple comparisons. For the double-angle plot diagrams, 95% confidence intervals were constructed according to formal bivariate statistical principles.16 Differences were considered statistically significant when the P value was less than 0.05. Statistical analyses were performed with the Xlstat sofware (version 2014.2.03, Addinsoft) and Sigmaplot software (version 12.5, Systat Software Inc.).
The study evaluated 68 eyes (48 patients). The mean age of the 17 women and 31 men was 66 years ± 9.5 (SD) (range 42 to 86 years). The mean axial length was 24.88 ± 1.48 mm (range 22.27 to 28.02 mm), and the mean IOL power was 17.6 ± 4.5 D (range 7.0 to 26.0 D). Forty-three eyes (63.2%) had WTR astigmatism, 22 eyes (32.4%) had ATR astigmatism, and 3 eyes (4.4%) had oblique astigmatism (30 to 60 degrees and 120 to 150 degrees). The mean corneal astigmatism was 2.34 ± 0.85 D (range 1.14 to 4.44 D). Table 1 shows the data on the implanted toric IOLs.
Absolute Error in Predicted Residual Astigmatism
Table 2 and Figure 1 show the absolute error in predicted residual astigmatism for each device and method of calculation. With the PCI device and the OLCR device, the median absolute error in predicted residual astigmatism ranged from 0.42 to 0.62 D and from 0.35 to 0.60 D, respectively. Application of the Baylor nomogram reduced the median absolute error for the Alcon and the Holladay toric calculators with the PCI device, from 0.60 to 0.50 D and from 0.62 to 0.50 D, respectively (both P <.001) and with the OLCR device, from 0.60 to 0.45 D and from 0.64 to 0.46 D, respectively (both P <.001). The Barrett toric calculator median absolute errors were 0.42 D and 0.35 D, respectively, which were lower than with the Alcon and Holladay toric calculators without (P <.001) or with (P = .002) the Baylor nomogram. The differences between the Alcon and the Holladay toric calculators were not significant (P=.998 and P=.920, respectively), as was the case when the Baylor nomogram was applied (P=.978 for the PCI device and P=.270 for the OLCR device).
Using the corneal topographer simulated K and mean K measurements, the median absolute error in predicted residual astigmatism ranged from 0.54 to 0.75 D and from 0.48 to 0.67 D, respectively. Application of the Baylor nomogram reduced the median absolute error for the Alcon and the Holladay toric calculators with the corneal topographer simulated K, from 0.72 to 0.61 D (P=.005) and from 0.75 to 0.59 D (P=.002) respectively, as well as with the corneal topographer mean K, from 0.65 to 0.49 D and from 0.67 to 0.50 D, respectively (P <.001). For the simulated K values, the Barrett toric calculator had a lower median absolute error in predicted residual astigmatism (0.54 D) than the Alcon and Holladay toric calculators without or with the Baylor nomogram (P <.001 and P=.013, respectively). The Barrett toric calculator had a significantly lower median absolute error in predicted residual astigmatism for the mean K values (0.48) than the Alcon and Holladay toric calculators without the Baylor nomogram (P <.001) and had a similar median absolute error when the Baylor nomogram was used (P=.850).
Using the Barrett toric calculator, the PCI device and the OLCR device had the lowest median absolute error in predicted residual astigmatism (0.42 D and 0.35 D, respectively). The corneal topographer simulated K had a median absolute error in predicted residual astigmatism of 0.54 D, which was significantly higher than the error with the PCI device and OLCR device (both P <.001). The corneal topographer mean K had a median absolute error in predicted residual astigmatism of 0.48 D, which was significantly higher than the error with the OLCR device (P=.008) but not the PCI device (P=.176). The differences between the median absolute error in predicted residual astigmatism of the PCI device and the OLCR device were not significant (P=.152), nor were the differences between the corneal topographer simulated K and corneal topographer mean K (P=.284). Figure 2 shows the proportion of eyes that had a median absolute error in predicted residual astigmatism of 0.50 D or less, 0.75 D or less, and 1.00 D or less. The highest proportions of eyes with a median absolute error in predicted residual astigmatism of 0.50 D or less, 0.75 D or less, and 1.00 D or less occurred using the Barrett calculator with the OLCR measurements (75.0%, 97.1%, and 100%, respectively).
Centroid Error in Predicted Residual Astigmatism
Table 2 shows the centroid error in predicted residual astigmatism for each device and method of calculation. The ATR centroid error in predicted residual astigmatism, ranging from 0.53 to 0.56 D, was observed when the Alcon and the Holladay toric calculators were used in all measuring devices. In contrast, applying the Baylor nomogram reduced the ATR centroid error in predicted residual astigmatism ranging from 0.21 to 0.26 D and using the Barrett toric calculator yielded a centroid error in predicted residual astigmatism ranging from 0.01 to 0.16 D; these differences were statistically significant (P <.001). The centroid error in predicted residual astigmatism for the PCI device and the OLCR device using the different methods of calculations are shown on double-angle plot diagrams in Figure 3, A, and Figure 3, B, respectively. The Barrett toric calculator had a lower centroid error (0.01 D) with the OLCR device than with the PCI device (0.10 D; P=.019) as well as lower SDs (0.31 D versus 0.37 D, respectively; P=.015).
Table 3 shows the centroid error in the predicted residual astigmatism in eyes with WTR corneal astigmatism (n = 43) and eyes with ATR corneal astigmatism (n = 22) measured by the OLCR device.
With-the-Rule Corneal Astigmatism
The Alcon and the Holladay toric calculators had ATR centroid errors in predicted residual astigmatism of 0.55 D and 0.59 D, respectively. The results with the Baylor nomogram lowered the centroid error in predicted residual astigmatism to 0.15 D and 0.19 D of ATR astigmatism, and the centroid error in predicted residual astigmatism for the Barrett toric calculator was close to zero (0.06 D) (P <.001).
Against-the-Rule Corneal Astigmatism
The centroid errors in the predicted residual astigmatism for the Alcon and the Holladay calculators were 0.48 D and 0.44 D ATR, respectively. Application of the Baylor nomogram resulted in an ATR centroid error in predicted residual astigmatism of 0.31 D and 0.28 D, respectively, whereas using the Barrett toric calculator resulted in a WTR centroid error in the predicted residual astigmatism of 0.16 D (P <.001).
The correction of corneal astigmatism during cataract surgery has become a standard of care.17 Toric IOLs have improved refractive outcomes; however, the results are not always predictable. Optimum correction of astigmatism requires accurate measurement, meticulous alignment of the toric IOL, and appropriate calculations. The aim of our study was to evaluate the accuracy of predicting toric IOL cylinder power by comparing 3 different toric IOL calculators and a nomogram using 2 automated keratometers and a corneal topographer. To avoid the noise associated with variable SIA and incorrect toric IOL alignment, measurements and calculations were performed using postoperative K values and the measured postoperative toric IOL axis alignment. Our results were derived by calculating the absolute and centroid astigmatic prediction errors.
The median absolute errors in predicted residual astigmatism were lower for the IOLMaster 500 PCI device (0.42 to 0.60 D) and the Lenstar LS 900 OLCR device (0.35 to 0.64 D) than with the Atlas corneal topographer using the simulated K (0.54 to 0.75 D) and the mean K (0.48 to 0.67 D) values. These differences, however, were more evident with the Baylor nomogram and the Barrett toric calculator. Previous studies8–10,18 compared the accuracy of different keratometers and topographers in assessing corneal astigmatism. Ignoring the posterior corneal astigmatism, however, can obscure differences between devices. In our study, the IOLMaster 500 and the OLCR Lenstar LS 900 keratometers had a clear advantage over the Atlas corneal topographer when we used the simulated K and mean K values, which suggests that K values derived from the corneal topographer are less reliable for toric IOL calculations. The Lenstar LS 900 device had a lower, but insignificant, median absolute error in predicted residual astigmatism than the IOLMaster 500 device with the Barrett toric calculator. Similarly, the percentage of eyes with an absolute error in predicted residual astigmatism of 0.50 D or less was higher with the Lenstar and Barrett toric calculator (75.0%) than with the IOLMaster (64.7%).
The absolute residual astigmatism prediction error reflects the clinical impact of the astigmatic outcome but does not consider the axis. The centroid residual astigmatism prediction error, however, which is displayed on double-angle plot diagrams calculated from the x and y components of the vector, considers both the astigmatic magnitude and direction, and it has been recommended as a preferred parameter to compare astigmatic outcomes after cataract and refractive surgery.15,19 When the Barrett toric calculator was used, the Lenstar LS 900 device had a significantly lower centroid and SD of the errors in the predicted residual astigmatism (D) than the IOLMaster device; that is, 0.01 @ 29 ± 0.31 and 0.10 @ 42 ± 0.37, respectively. These results can be attributed to the 32 measuring points arranged in 2 concentric rings of the Lenstar keratometer as opposed to the 6 measuring points of the IOLMaster keratometer. Another potential advantage of the Lenstar device is the strict validation criteria, which can be applied for each measurement (eg, SD values for each set of keratometries [flat and steep] and axes).
The method to calculate toric IOL power has a key role in achieving accurate prediction results in the setting of toric IOL implantation. The most widely used method is probably the online toric IOL calculator by Alcon,C which uses a fixed ratio to predict the toric IOL power at the corneal plane. This ratio, however, varies with the ELP and cylinder power of the IOL.2,13,20 In contrast to the Alcon calculator, the Holladay toric calculator uses the predicted preoperative ELP to calculate the actual toric IOL power at the corneal plane and theoretically should be more accurate. However, both calculators showed similar results in our current study. Our findings, therefore, suggest that the consideration of ELP alone may not be adequate to optimize the prediction of the surgical outcomes with toric IOLs. Using the Alcon and the Holladay toric calculators led to ATR centroid errors in the predicted residual astigmatism ranging between 0.53 D and 0.56 D. These results correlate those in a previous study by Koch et al.,8 and the values derived from those calculators would lead to a recommended toric IOL power that would result in significant ATR residual astigmatism.
The relationship between the anterior cornea and posterior cornea was first described in 1890 by Javal21 and was known as Javal’s rule, which was later simplified in 1988 by Grosvenor et al.22 and confirmed by several authors for diverse populations23–27 as well as for pseudophakic eyes.28,29 We evaluated 2 methods that take into account the effect of the posterior corneal astigmatism. The Baylor nomogram considers the mean values of posterior corneal astigmatism8 and is intended to be used with calculators, such as the Alcon or Holladay, that do not consider the posterior cornea. The Barrett toric calculatorD uses the Barrett Universal II formula to calculate the toric IOL power at the corneal plane and incorporates a mathematic model that uses the keratometry measurements (derived from anterior corneal measurements) to calculate the posterior corneal astigmatism and therefore requires no adjustment. In our study, both methods achieved lower centroid errors in predicted residual astigmatism (range from 0.21 to 0.26 D and from 0.01 to 0.16 D, respectively) when all measuring devices were applied. These differences were significant compared with the Alcon and the Holladay toric calculators (P<.001). The Barrett toric calculator had a lower median absolute error in predicted residual astigmatism than the Baylor nomogram when the IOLMaster 500 device (0.42 D versus 0.50 D) and the Lenstar LS 900 device (0.35 D versus 0.45 D) were used (P=.002). The centroid errors were also lower (0.10 D versus 0.23 D and 0.01 D versus 0.22 D, respectively) (P<.001).
In their study, Koch et al.12 found that the astigmatism of the posterior cornea correlates with WTR astigmatism but not with ATR astigmatism. In our subgroup analysis comparing WTR eyes and ATR eyes, the Alcon and the Holladay toric calculators had a similar effect of approximately 0.55 to 0.59 D ATR centroid error in the predicted residual astigmatism in both subgroups. These results correlate well with findings by Koch et al.8 for WTR astigmatism and partially for ATR astigmatism. Applying the Baylor nomogram improved the outcome to an ATR centroid prediction error ranging from 0.15 to 0.19 D in the WTR subgroup and an ATR centroid prediction error ranging from 0.28 to 0.31 D in the ATR subgroup. The Barrett calculator had a centroid error in predicted residual astigmatism of 0.06 D ATR in the WTR subgroup and 0.16 D WTR in the ATR subgroup. In our dataset, the results suggest that for eyes with WTR and ATR corneal astigmatism, the Baylor nomogram tends to undercorrect corneal astigmatism, which might result in minor to moderate postoperative ATR residual astigmatism. The Baylor nomogram, however, has a WTR target residual astigmatism ranging from 0.0 to 0.4 D, which tends to negate this effect. The Barrett toric calculator shows a centroid error that is close to zero for eyes with WTR corneal astigmatism and a minimal overcorrection for eyes with ATR corneal astigmatism, which may result in minor WTR residual astigmatism in the latter case.
A limitation of our study is that it included only 22 eyes with ATR astigmatism and 3 eyes with oblique astigmatism. Further studies of greater numbers of eyes with ATR and oblique astigmatism are needed to evaluate in greater depth the role of the corneal astigmatic axis in toric IOL calculations. We also recognize that our study only considered devices that measure anterior corneal astigmatism. We therefore recommend further studies to evaluate the error in the predicted residual astigmatism using devices based on Scheimpflug cameras or optical coherence tomography that are able to measure posterior corneal astigmatism.
In conclusion, the Lenstar LS 900 and IOLMaster 500 devices were better than the Atlas corneal topographer, while the Alcon and Holladay toric calculators adjusted with the Baylor nomogram and the Barrett toric calculator were better than the standard Alcon and Holladay toric calculators. In our study, the most accurate prediction of residual astigmatism was achieved with the Barrett toric IOL calculator in combination with Lenstar LS 900 keratometry. The outcome of toric IOL implantation can be optimized by using an appropriate toric IOL calculator and an appropriate measuring device. Further studies are needed to compare the performance of different toric calculators when adjusted by direct measurements of the posterior corneal curvature.
What Was Known
- The results of several keratometry devices in assessing the corneal astigmatic power are comparable.
- The use of devices that measure the anterior cornea only with standard toric IOL calculators tend to result in undercorrection of eyes with ATR astigmatism and overcorrection of eyes with WTR astigmatism.
What This Paper Adds
- The PCI and OLCR keratometers were better than the corneal topographer simulated K and mean K values for toric IOL calculations, with the latter being more accurate.
- The Baylor toric IOL nomogram or the Barrett toric calculator significantly reduced errors in residual astigmatism predictions in toric IOL calculations.
- The OLCR device and the Barrett toric calculator provided the lowest residual astigmatism prediction errors compared with other devices and methods of calculation.
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