#### Abstract

Given that a previous study found that corneal asphericity influences the refractive outcome of intraocular lens (IOL) power calculation by means of thin-lens formulas in eyes with spherical IOLs, the authors aimed to verify whether such influence can also be observed in eyes with aspherical IOLs.

In this retrospective comparative case series, IOL power was calculated with the Haigis, Hoffer Q, Holladay 1, and SRK/T formulas in two groups of eyes undergoing phacoemulsification and implantation of an aspherical IOL (Acrysof SN60WF; Alcon Laboratories, Inc., Fort Worth, TX). For each formula, the refractive prediction error was calculated once the constants had been optimized. Biometric data were obtained by partial coherence interferometry in one group and immersion ultrasound biometry and corneal topography in the other. Corneal asphericity was assessed by two different corneal topographers in the optical biometry group (Magellan; Nidek, Gamagori, Japan) and ultrasound biometry group (Keratron, Optikon 2000 Spa, Rome, Italy).

The mean Q-value was −0.12 ± 0.08 in the optical biometry group (n = 51) and −0.22 ± 0.14 in the ultrasound biometry group (n = 79). In both groups, linear regression disclosed a statistically significant correlation between the Q-value and the prediction error (the only exception being the SRK/T formula). More negative Q-values were correlated to a positive prediction error, indicating a myopic outcome for prolate corneas. However, the correlation coefficients were lower than those previously reported for spherical IOLs.

Corneal asphericity also influences the refractive outcomes of IOL power calculation by thinlens formulas when aspherical IOLs are implanted, although this influence is exerted to a lesser degree compared to spherical IOLs.

**[ J Refract Surg. 2017;33(7):476–481.]**

Intraocular lens (IOL) power calculation is not yet a perfect science. Refractive prediction errors greater than ±0.50 diopters (D) occur in approximately 20% to 30% of eyes undergoing cataract surgery and IOL implantation,^{1–7} and are likely to affect patient satisfaction, especially with multifocal IOLs. There are different sources of these errors. In 2008, Norrby pointed out that the prediction of the IOL position plays a major role in this context,^{8} and newer formulas have focused their attention on this issue.^{9} Other factors are the assessment of postoperative refraction, pupil diameter, corneal anterior/posterior radius ratio,^{8} and IOL design.^{10} In 2015, we showed that corneal asphericity (Q-value) may also affect the accuracy of the prediction of refractive outcome after IOL implantation.^{11} In a group of eyes that had been implanted with a spherical IOL (Acrysof SA60AT; Alcon Laboratories, Inc., Fort Worth, TX), we found that prolate corneas were likely to have a more myopic outcome, whereas oblate corneas had a higher chance of a more hyperopic refraction. In a subsequent letter to the editor about this study, Holladay^{12} suggested that our results might have been related to the choice of IOL and that the effect of corneal asphericity would disappear with an aspherical IOL.

This study was designed to investigate whether Holladay's hypothesis is true (ie, whether the influence of corneal asphericity on the results of IOL power calculation would not be detected in eyes with aspherical IOLs).

### Patients and Methods

This was a retrospective analysis including two series of consecutive eyes that underwent phacoemulsification and implantation of the same one-piece IOL (AcrySof SN60WF). If both eyes of the same patient underwent surgery, only the first one was considered. Before being included in the study, all patients were informed of its purpose and gave their written consent. The study methods adhered to the tenets of the Declaration of Helsinki for the use of human participants in biomedical research and the study was approved by the G.B. Bietti Foundation IRCCS Ethics Committee.

The first series of patients (the optical biometry group) was operated on by a single surgeon (DSL) in Rome, Italy, and the second series (the ultrasound biometry group) by two surgeons (GS, PB) in Bologna, Italy. The surgical technique was the same for all cases and included phacoemulsification through a 2.2-mm temporal incision and implantation of a monofocal aspherical IOL (Acrysof SN60WF).

Exclusion criteria were: prior corneal or intraocular surgery, keratoconus and any other corneal disease, contact lens use during the past month, and postoperative corrected distance visual acuity worse than 0.8 (Snellen 20/30) for any reason.

#### IOL Power Calculation

The IOL power was calculated by means of the Haigis, Hoffer Q, Holladay 1, and SRK/T formulas. In the optical biometry group, axial length was measured by partial coherence interferometry (IOLMaster 500; Carl Zeiss, Jena, Germany) and anterior chamber depth from the epithelium to the lens and corneal power were measured by the IOLMaster 500. In the ultrasound biometry group, axial length and anterior chamber depth measurements were performed by Ocuscan RX (Alcon Laboratories, Inc.) ultrasound immersion biometry and corneal power was measured with a Placido disk-based corneal topographer (Keratron; Optikon 2000 Spa, Rome, Italy). It uses an arc-step algorithm to reconstruct the corneal profile as a series of arcs that would reflect the rays from the mires to the keratoscope lens.^{13,14} Twenty-six rings are projected onto the cornea to calculate the simulated keratometry value by converting the measured radius into diopters using the standard keratometric refractive index of 1.3375. The Keratron calculates the simulated keratometry as the mean between the power of the flattest meridian at the 3-mm diameter and the power of the meridian 90° away from it, independently of its curvature (so that the latter is not necessarily the steepest meridian). According to a previous study, the corneal power and axial length measurements by the two techniques do not show statistically significant differences.^{15}

A final evaluation was performed by assessing the subjective refractive outcomes at 1 month postoperatively, which is when refractive stability can be expected with small-incision clear cornea surgery and this type of IOL.^{16–18} The subjective refraction was measured by two experienced ophthalmologists (GS, DSL) with the same room lighting conditions (200 lux) used for our previous study.^{11}

Predictions made using the Haigis, Hoffer Q, Holladay 1, and SRK/T formulas^{19–22} were retrospectively optimized by adjusting their respective constants to give the series a mean prediction error of zero, according to the method described by Hoffer^{23} and Olsen.^{24} As a result, it was possible to evaluate the statistical error as representing the optimal prediction error rather than offset errors related to incorrect lens constants or systematic errors in the measuring environment. To calculate the refractive prediction error, the postoperative refraction was subtracted from the predicted refraction (based on the IOL actually implanted) according to each formula. The mean prediction error, the median absolute error, and the mean absolute error were calculated, as well as the percentage of eyes with a prediction error within ±0.50 diopters (D).^{20,25}

#### Corneal Asphericity Measurement

In the optical biometry group, preoperative anterior corneal surface asphericity Q-values were obtained by means of a Placido disk corneal topographer (Magellan; Nidek, Gamagori, Japan). This instrument provides a coefficient of eccentricity, which corresponds to “e” and had to be converted into the more commonly used Q-value by means of the equation^{26}: Q-value = −e2.

In the ultrasound biometry group, the preoperative Q-values were directly obtained by means of the abovementioned Keratron corneal topographer. Q-values are negative (−1 < Q < 0) for prolate corneas, in which the central curvature is steeper than the peripheral curvature, and positive (Q > 0) for oblate corneas, in which the central curvature is flatter than the peripheral curvature.

#### Statistical Analysis

Statistical analysis was performed using Microsoft Excel (Microsoft Corporation, Redmond, WA) and Med-Calc for Windows (version 12.7; MedCalc Software, Ostend, Belgium). Linear regression analysis was performed to investigate whether any relationship existed between the arithmetic error in refraction prediction and the Q-value. The coefficient of determination *R*^{2} was used to express the proportion of the variation in the dependent variable (ie, the refractive prediction error) explained by the regression model. In this context, the refraction prediction error was negative for cases with postoperative hyperopic refraction and positive for cases with postoperative myopic refraction. A *P* value of less than .05 was considered statistically significant. The normality of the distribution of data was assessed using the Kolmogorov–Smirnov test.

### Results

Fifty-one patients (29 women [57%] and 22 men [43%], mean age: 71.1 ± 10.4 years) were enrolled in the optical biometry group and 79 patients (45 women [60%] and 34 men [40%], mean age: 72.7 ± 9.6 years) in the ultrasound biometry group. Their mean measurements are reported in **Table 1**.

Table 1: Mean ± SD Values of Biometric Data |

The prediction error, median absolute error, mean absolute error, and percentage of eyes with a prediction error of ±0.50 D or less are reported for each tested formula in **Table 2**. The mean Q-value was −0.12 ± 0.08 (range: −0.44 to +0.06) in the optical biometry group and −0.21 ± 0.14 (range: −0.77 to +0.06) in the ultrasound biometry group. In both groups, linear regression showed a statistically significant correlation between the prediction error and the Q-value provided by corneal topography (**Table 3**). In all cases, linear regression revealed that corneas with more negative Q-values (ie, prolate corneas) were more likely to induce a myopic outcome (ie, a positive prediction error), whereas corneas with more positive Q-values (ie, oblate corneas) were more likely to induce a hyperopic outcome (ie, a negative prediction error). **Figure 1** illustrates the regression line and the 95% prediction interval for one of the formulas (the Hoffer Q) in both groups.

Table 2: Refractive Outcomes of IOL Power Calculation With the Formulas Evaluated |

Table 3: Correlation Coefficients Showing the Relationship Between Corneal Asphericity (Q-value) and the Refractive Prediction Error |

**Table 3** also reveals that the relationship between the Q-value and the prediction error was stronger in the optical biometry group; the coefficient of correlation *r* was close to −0.5 and the *P* value ranged from less than .0001 to .0012. In the ultrasound biometry group, the relationship was weaker; the coefficient of correlation was close to −0.2 and the *P* value ranged between .0208 and .0479. From a clinical point of view, this means that in both groups the prediction error was close to zero with a Q-value close to the average (ie, between −0.1 and −0.2). According to linear regression, in the optical biometry group a prediction error of 0.50 D (in a myopic direction) would be expected with a Q-value of just −0.3, whereas in the ultrasound biometry group the same prediction error would be expected with a Q-value of −0.9.

### Discussion

In this study, we showed that corneal asphericity can influence the outcomes of IOL power calculation by means of thin-lens formulas, even when aspherical IOLs are implanted. In our previous study, we analyzed a sample of eyes with spherical IOLs and found that prolate corneas (whose curvature is steeper in the center than in the paracentral area) are more likely to induce a myopic outcome, whereas the opposite occurs with oblate corneas (whose curvature is flatter in the center than in the paracentral area).^{11} We postulated that this is due to the difference in curvature between the paracentral corneal area, where keratometric measurements are taken with keratometers and corneal topographers, and the central corneal area, where the visual axis passes.

According to Holladay,^{12} our results may have depended on the choice of a spherical IOL and the influence of corneal asphericity on IOL power calculation might disappear with the implantation of aspherical IOLs. However, this study shows that corneal asphericity exerts a similar influence on IOL power calculation in eyes with aspherical IOLs. Moreover, the fact that we obtained the same results in two completely separate samples (where biometric data were obtained using different instruments) reinforces our findings and further supports the role of corneal asphericity in IOL power calculation.

It is interesting to compare the results of the ultrasound biometry group to those of the previous study^{11} because in both cases corneal asphericity was measured with the same topographer and the sample size was similar. Such a comparison reveals that using aspherical IOLs reduced the correlation coefficient because the *R*^{2} coefficient decreased from values between 0.1481 and 0.2630 to values between 0.04987 and 0.06924. Hence, using aspherical IOLs does not eliminate but may reduce the effect of corneal asphericity on postoperative refraction. Accordingly, linear regression showed that for each 0.1 difference of the Q-value, the prediction error is lower with aspherical than with spherical IOLs. For example, with a spherical IOL and the Holladay 1 or Hoffer Q formula, a prediction error close to zero (0.02 D) would be expected with the average Q-value (−0.20) and a prediction error close to 0.50 D (0.57 and 0.61 D, respectively, always with a more myopic outcome than expected) would be expected with a Q-value of 0.60 (prolate cornea). With the same formulas and an aspherical IOL, the prediction error would be close to zero (0.01 D) with the average Q-value and close to 0.25 D (0.27 and 0.30 D, respectively) with a Q-value of 0.6.

In addition, four secondary outcomes deserve our attention. First, because aspherical IOLs compensate for the positive spherical aberration in the cornea, they are also likely to provide more accurate refractive results than spherical IOLs. With all four formulas, the median absolute error was within 0.21 and 0.22 D in the ultrasound biometry group, whereas it ranged between 0.23 and 0.30 in eyes with spherical IOLs whose power was calculated using the same instruments.^{11}

Second, we were surprised by the relatively poor performance of partial coherence interferometry, especially when compared to the results obtained by immersion ultrasound biometry and corneal topography (**Table 2**). It was not our purpose to compare optical biometry to ultrasound biometry, and for this reason we did not focus our attention on this issue. However, it should be noted that the percentage of eyes with a prediction error of ±0.50 D or less in this study is similar to those previously obtained with partial coherence interferometry by Hoffer et al.^{4} (56%), Olsen^{5} (62.5%), and Srivannaboon et al.^{7} (68%).

Third, the distribution of the average axial length toward myopic values (mean value: 24.51 mm in the optical biometry group and 24.07 mm in the ultrasound biometry group) might have influenced the accuracy of the tested formulas. For example, this is the likely reason why the Hoffer Q formula, which is known to provide better results in short (< 22 mm) eyes,^{27} did not perform as well as the SRK/T formula. In both samples, short eyes (< 22 mm) were a minority (1 of 51 in the optical biometry group, 1 of 79 in the ultrasound biometry group).

Fourth, the mean anterior chamber depth was shallower in eyes measured by partial coherence interferometry than in eyes measured by immersion ultrasound biometry. Although this result may depend on the different samples, it could also be related to the fact that the IOLMaster is known to provide lower values of anterior chamber depth compared to other instruments.^{4,28–30}

The current study is limited by the fact that, due to the retrospective nature of the investigation, we did not measure pupil size and ocular spherical aberration when subjective refraction was assessed postoperatively. It would be logical to observe a major influence of corneal asphericity in eyes with larger pupils and this will be the purpose of a new prospective study. Moreover, we investigated only one IOL model. It would be interesting to confirm our results with other IOLs inducing a different negative spherical aberration.

Our data suggest that corneal asphericity also influences the refractive outcomes of IOL power calculation by thin-lens formulas when aspherical IOLs are implanted, although this influence is less than with spherical IOLs.

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Mean ± SD Values of Biometric Data

IOL power (D) | 19.72 ± 4.35 | 20.22 ± 3.04 |

Keratometry (D) | 43.51 ± 1.63 | 43.51 ± 1.11 |

Q-value | −0.12 ± 0.08 | −0.21 ± 0.14 |

Anterior chamber depth (mm) | 3.19 ± 0.45 | 3.31 ± 0.35 |

Axial length (mm) | 24.51 ± 2.11 | 24.07 ± 1.20 |

Refractive Outcomes of IOL Power Calculation With the Formulas Evaluated

Haigis | 0.00 ± 0.63 | 0.32 | 0.43 | 79.2 (89.6) | 0.01 ± 0.41 | 0.21 | 0.30 | 83.1 (96.2) |

Hoffer Q | 0.07 ± 0.69 | 0.39 | 0.48 | 64.7 (94.1) | 0.02 ± 0.41 | 0.22 | 0.30 | 83.5 (96.2) |

Holladay 1 | 0.11 ± 0.68 | 0.37 | 0.48 | 66.7 (92.2) | 0.01 ± 0.37 | 0.22 | 0.28 | 88.6 (98.7) |

SRK/T | 0.04 ± 0.62 | 0.35 | 0.46 | 60.8 (92.2) | −0.01 ± 0.35 | 0.21 | 0.26 | 91.1 (97.5) |

Correlation Coefficients Showing the Relationship Between Corneal Asphericity (Q-value) and the Refractive Prediction Error

^{2} | ^{2} | |||||
---|---|---|---|---|---|---|

Haigis | −0.5257 | 0.2763 | .0001 | −0.2631 | 0.06924 | .0208 |

Hoffer Q | −0.5523 | 0.3050 | < .0001 | −0.2463 | 0.06066 | .0287 |

Holladay 1 | −0.4559 | 0.2078 | .0008 | −0.2503 | 0.06266 | .0261 |

SRK/T | −0.4415 | 0.1949 | .0012 | −0.2233 | 0.04987 | .0479 |