Toric IOL Calculation in Eyes With High Posterior Corneal Astigmatism

Patients and Methods

This study involved a retrospective review of consecutive medical records of patients who had cataract surgery with implantation of toric IOLs whose PCA was 0.80 D or greater. The surgeries were performed by a single surgeon (GK) at Ein-Tal Eye Center, Tel Aviv, Israel, from July 2012 to July 2019. The institutional ethics committee of the Meir Medical Center, Kfar-Saba, Israel, approved this study.

Inclusion criteria included: implantation of a toric IOL, preoperative biometric measurements and dual-zone autokeratometry by the Lenstar device (Lenstar LS900; Haag-Streit AG), measurements of PCA with the Scheimpflug camera (Pentacam; Oculus Optikgeräte GmbH) graded by the instrument as “OK,” postoperative manifest refraction at least 1 month after surgery with a corrected distance visual acuity of better than 20/40, and the axis of the toric IOL position recorded at the postoperative visit. The toric IOL position was photographed with a slit-lamp digital color camera (CSO Elite Mega Digital Vision camera; Sky Optic). Then, the IOL’s axis was evaluated using the Goniotrans software (Eventos Médicos y Sociales, SL) that integrates a virtual protractor over an eye picture by dragging the radial line to the position of the toric lens axis marks on the angle pattern. Exclusion criteria were any previous ocular surgery, other ophthalmic pathology, perioperative complications, postoperative toric IOL tilt under slit-lamp examination, and incomplete surgical or clinical data.

Four methods of calculating a toric IOL were compared in this study: (1) keratometric measurement adjustment using the Abulafia-Koch formula, as described by Abulafia et al,¹³ (2) integration of PCA measured by the Pentacam, with the keratometric astigmatism measured by the Lenstar using vector summation (vector summation), (3) the Barrett toric calculator based on predicted PCA (Barrett’s predicted PCA), and (4) the Barrett toric calculator based on measured PCA (Barrett’s measured PCA).

Predicted postoperative refractive astigmatism for the implanted toric IOL power and the measured axis was calculated using each method as follows. First, the amount and direction of the corneal astigmatism requiring correction were determined for each method of calculation. Personalized centroid corneal surgically induced astigmatism (SIA-cornea), which had been calculated previously, was used in all calculations (right eye: 0.14 D @ 138 and left eye: 0.11 D @ 119). Second, the equivalent of the astigmatism corrected by the toric IOL at the corneal plane was calculated. Calculations of the toric IOL cylinder power at the corneal plane with the Abulafia-Koch adjustment and with vector summation were performed according to the meridional analysis method¹⁷ based on the Holladay 1 formula.¹⁸ IOLs’ Surgeon Factor constants were according to the recommendation of the User Group for Laser Interference website ( http://ocusoft.de/ulib). For the Barrett toric calculator, the value was taken directly from the calculator output using its integral Lens Factor constants, when available, or using the A-constant in unavailable IOLs. Finally, 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 estimated corneal astigmatism by each method.

Astigmatic prediction errors were calculated as the difference between the actual postoperative refractive outcomes adjusted to the corneal plane and the predicted residual astigmatism at the corneal plane for the implanted IOL by each calculation method. Vector analysis was used for these calculations by doubling the angle and performing separate analysis of the x and y Cartesian coordinates.^19,20 Afterward, these data were inserted in double-angle plots and bivariate analysis was performed.^20,21 The centroid and absolute astigmatic prediction errors and the number of eyes with an absolute prediction error of 0.25 D or less, 0.50 D or less, 0.75 D or less, 1.00 D or less, and 1.50 D or less were calculated for all methods of calculation.

Results

A total of 173 cataract extraction surgeries with implantation of toric IOLs were performed by the surgeon during the study period. Seventeen eyes (10%) of 13 patients met the inclusion criteria and were enrolled into the study. Patients’ baseline characteristics are presented in Table 1. Implanted toric IOL models were as follows: 10 Acrysof SN6AT and 1 Acrysof SN6AD (Alcon Laboratories, Inc), 3 Tecnis Symfony ZXT (Johnson & Johnson), 2 Bi-Flex 677TA (Medicontur), and 1 Vistor (Hanita Lenses).

Table 1: Patient Characteristics, Biometry Measurements, and Implanted IOLs

Corneal Astigmatism Measurements

The mean absolute keratometric astigmatism was 4.10 ± 1.55 D (median: 3.90 D, range: 2.07 to 7.98 D). Mean centroid keratometric astigmatism was 3.65 ± 2.46 D @ 89°. All eyes had with-the-rule keratometric astigmatism. The mean absolute PCA was 0.91 ± 0.12 D (median: 0.90 D, range: 0.80 to 1.10 D) and the mean centroid PCA was 0.82 ± 0.42 D @ 87° with a vertical orientation of the steep meridian in all eyes. A non-significant weak correlation was found between the magnitude of keratometric astigmatism and PCA power (correlation coefficient = 0.400, P = .111) (Figure 1). Cohort analysis of toric IOLs during the study period in our center (data not published) showed a moderate correlation between the magnitude of keratometric astigmatism and PCA (correlation coefficient = 0.487, P < .001).

Figure 1. Correlation between preoperative measurements of keratometric astigmatism and posterior corneal astigmatism.

Postoperative Refractive Astigmatism Prediction Error

The errors in predicted postoperative refractive astigmatism for each method of calculation are displayed in Table 2. The mean absolute error was significantly lower with Barrett’s measured PCA (0.55 ± 0.38 D) than the Abulafia-Koch formula (0.80 ± 0.36 D, P = .011) and vector summation (0.69 ± 0.33 D, P = .022). Barrett’s predicted PCA showed a mean absolute prediction error of 0.65 ± 0.31 D and was significantly better than the Abulafia-Koch formula (P = .006). All other differences between the calculation methods did not reach a level of significance.

Table 2: Mean Absolute and Centroid Errors in Predicted Postoperative Refractive Astigmatism for Toric IOL Calculations With Predicted and Measured PCA

Mean centroid prediction error with Barrett’s measured PCA (0.14 ± 0.66 D @ 70°) and Barrett’s predicted PCA (0.14 ± 0.73 D @ 179°) was statistically significantly lower than with the Abulafia-Koch formula (0.39 ± 0.80 D @ 179°, P < .001 and .006, respectively) and vector summation (0.35 ± 0.70 D @ 5°, P < .001 and .031, respectively). Although Barrett’s measured PCA exhibited a with-the-rule centroid error, Barrett’s predicted PCA yielded an against-the-rule centroid prediction (P = .002). Figure A (available in the online version of this article) displays the double-angle plots of the error in the predicted astigmatism of each method.

Figure A. Double-angle plots of the error of the predicted refractive astigmatism for (A) Abulafia-Koch formula, (B) vector summation of kerato-metric astigmatism and posterior corneal astigmatism (PCA), (C) Barrett’s toric calculator based on predicted posterior corneal astigmatism, and (D) Barrett’s toric calculator based on measured posterior corneal astigmatism. D = diopters

The percentage of eyes with prediction errors within 0.25 D or less was higher for Barrett’s measured PCA (29.4%) than for the Abulafia-Koch formula (0%, P = .025), vector summation (0%, P = .025), and Barrett’s predicted PCA (5.9%, P = .046). No significant differences were seen between the rates of errors within 0.50 D or less (52.9%, 29.4%, 35.3%, and 35.3%, respectively), 0.75 D or less (70.6%, 47.1%, 64.7%, and 64.7%, respectively), 1.00 D or less (88.2%, 76.5%, 82.4%, and 94.1%, respectively), and 1.50 D or less (100%, 94.1%, 94.1%, and 100%, respectively) (Figure 2).

Figure 2. The proportion of eyes with errors in predicted residual astigmatism within 0.25 diopters (D) or less, 0.50 D or less, 0.75 D or less, 1.00 D or less, and 1.50 D or less. *Barrett’s measured PCA > A-K, vector summation and Barrett’s predicted PCA. PCA = posterior corneal astigmatism; A-K = Abulafia-Koch formula

Discussion

The contribution of the posterior corneal curvature to total corneal astigmatism has been discussed extensively in the literature.^6,17,22,23 Previous studies have described the precision of the astigmatic prediction with PCA measurements. Savini and Naeser⁸ demonstrated that PCA exerts the highest influence on the astigmatic prediction error after toric IOL implantation in a model evaluating PCA, surgically induced cor-neal astigmatism, IOL orientation, and effective lens position. Hoffmann et al⁷ reported that combining the data of keratometry, anterior topography, and posterior tomography measurements yields the best results for toric IOL power calculations. Similarly, our group showed that incorporating posterior tomography with anterior keratometry using vector summation improved postoperative refractive astigmatism outcomes after toric IOLs implantation.²⁴ Recognition of the significance of PCA in the calculation of toric IOLs has led to the development of adjustment methods that take posterior astigmatism into account.^6,15,25,26 Abulafia et al¹³ developed an adjustment formula for the x and y components of the keratometric astigmatism using linear regression to calculate the estimated total corneal astigmatism based on standard keratometry measurements. Barrett addressed this issue by introducing the Barrett toric calculator, which uses an advanced model to predict PCA based on anterior corneal measurements.¹¹ However, Barrett’s method has not been published.

Those solutions provide accurate refractive outcomes for the majority of cases. However, in extreme cases, such as those we present in the current study, relying on average adjustments may be less accurate. To our knowledge, no study has evaluated the performance of mathematic methods to estimate PCA in comparison to its direct measurement in cases of high PCA.

Savini et al²⁷ have shown PCA exceeds 0.50 and 1.00 D in 55.4% and 5.7% of eyes, respectively. In our cohort, 10% of eyes had high PCA (0.80 D or greater). Moreover, we observed that the amounts of keratometric astigmatism and PCA do not necessarily correlate. Therefore, the predicted PCA based solely on the magnitude of keratometric astigmatism could be inaccurate. Incorporation of direct measurements of the posterior cornea into the toric IOL calculation using Barrett’s calculator resulted in the lowest absolute prediction error, reaching statistical significance in comparison with the Abulafia-Koch formula and vector summation. Furthermore, Barrett’s measured PCA led to a higher percentage of eyes with a prediction error within 0.25 D or less compared with the other three methods. In addition, the centroid error was the smallest using Barrett’s calculator with measured and predicted PCA. However, although the predicted PCA option resulted in an against-the-rule error, similar to the other methods evaluated, Barrett’s measured PCA was the only one to yield a with-the-rule error.

Interestingly, although vector summation incorporates measured PCA, it was not superior to Barrett’s predicted PCA, which uses an empiric PCA calculation. A possible explanation is the use of the meridional analysis method²⁸ with the Holladay 1 formula for the calculation of the toric power at the corneal plane in the vector summation analysis. In contrast, the Barrett toric calculator is based on the Barrett universal II formula, which is considered more accurate than the Holladay 1 formula.^29–32

There are some limitations to our study, beginning with its retrospective nature. Second, the study included only 17 eyes, making it underpowered. Further studies on greater numbers of eyes are needed to evaluate in greater depth the performance of toric IOL calculations in eyes with high PCA. Another limitation is that direct measurements of the total cornea were not analyzed, but rather only direct measurement of the PCA was integrated. Finally, there is a possible influence of the SIA-cornea on the analysis. The SIA-cornea used in our analysis is the mean personalized SIA that has been previously calculated for the surgeon for routine preoperative toric IOL calculations. However, the variations in the astigmatic effect of the surgical incision could possibly lead to deviations in this parameter in individual cases. Nonetheless, using preoperative measurements with a personalized SIA-cornea allows imitation of real clinical practice.

Considering the effect of posterior corneal astigmatism reduces the errors in predicted residual astigmatism in toric IOL calculations. However, because high PCA can be found in a wide range of keratometric astigmatism cases, direct measurement of the posterior cornea might have an advantage over methods that use mathematical models to account for its effect. We suggest that in cases of high PCA (0.8 and above), toric calculators and adjustment formulas may not fully compensate for the posterior astigmatism, especially in cases with a relatively low keratometric astigmatism. As a result, the recommended IOL might not be highly accurate. We therefore suggest considering directly measuring the PCA and considering its use in patients with high PCA as an optional approach to tackle a potential problem. Further research that evaluates prospective refractive outcomes of the clinical application of these methods with a larger dataset is desirable to draw conclusive inferences.