#### Abstract

To compare the accuracy of intraocular lens (IOL) power calculation based on standard keratometry (K) and the new Total Keratometry (TK).

A post-hoc analysis of study data based on 145 pseudophakic astigmatic eyes was conducted. The absolute prediction error (APE) of spherical equivalent (SE) and cylinder (CYL) was calculated based on K and TK (including posterior corneal surface) data recorded 6 weeks after IOL implantation. APE was calculated as the difference between the postoperative refraction and the refractive error predicted by three classic IOL calculation methods (Haigis/Haigis-T, Barrett Universal II, Barrett Toric Calculator) and two new formulas developed for TK (Barrett TK Universal II, Barrett TK Toric). For APE in SE, the Haigis-T (K versus TK) and Barrett Universal II (K) versus Barrett TK Universal II (TK) were compared. For APE in CYL, the Haigis-T (K versus TK) and Barrett Toric Calculator (K) versus Barrett TK Toric formula (TK) were compared.

Mean APE in SE and CYL was lower based on TK values compared to K, with a mean APE difference (K − TK) of 0.011 ± 0.107 diopters (D) (SE Haigis-T; 95% confidence interval [CI]: −0.004 to infinity), 0.016 ± 0.113 D (SE: Barrett Universal II versus Barrett TK Universal II; 95% CI: 0.0005 to infinity), 0.103 ± 0.173 D (CYL: Haigis-T; 95% CI: 0.0791 to infinity), and 0.020 ± 0.148 D (CYL: Barrett Toric versus Barrett TK Toric; 95% CI: −0.0002 to infinity). APE in SE was within ±0.50 D in 86% (Barrett TK Universal II) versus 84% (Barrett Universal II) of eyes. APE in CYL was within ±0.50 D in 58% (Haigis from TK) versus 44% (Haigis from K) of eyes.

In comparison to standard K, a higher prediction accuracy can be expected by using TK values along with the two newly developed formulas. TK values are compatible with standard IOL power calculation formulas and existing optimized IOL constants.

**[ J Refract Surg. 2019;35(6):362–368.]**

Recently, a large multinational database study on intraocular lens (IOL) predictability including 282,811 cases showed that the mean absolute spherical equivalent (SE) prediction error after cataract surgery was 0.42 diopters (D) and 72% of eyes were within ±0.50 D of predicted SE.^{1} In addition to various factors, such as coexisting eye diseases and surgical complications, the authors stated that the influence of postoperative residual astigmatism was considerable in their study.^{1} Although toric intraocular lenses (IOLs) are a major advance in compensating corneal astigmatism in the course of cataract surgery, residual postoperative astigmatism remains a concern, with more than one-third of patients not reaching the targeted refraction after toric IOL implantation.^{2} One cause of unexpected refractive cylinder after toric IOL implantation is the incorrect estimation of total corneal astigmatism, especially in eyes with low astigmatism.^{2}

Today, standard keratometry relies purely on measurements of the anterior corneal surface.^{3} However, the anterior and posterior curvature and corneal thickness contribute to the total refractive power of the human cornea. Previous studies showed that ignoring the posterior corneal surface may lead to inaccuracies in total corneal power and astigmatism estimation in some eyes and that selecting toric IOLs based on anterior corneal measurements only and neglecting the effects of actual posterior corneal curvature could lead to significant postoperative overcorrection or undercorrection.^{4–8} This is especially critical in toric multifocal IOLs, where it is important to minimize the residual refractive error.^{9} By using nomograms such as the Baylor nomogram or the Barrett Toric Calculator,^{10,11} total corneal astigmatism can be predicted based on the power and axis of the anterior corneal astigmatism. However, these methods are based on mathematical extrapolation only and thus cannot take outliers and irregularities into account (eg, occurring in eyes after laser-assisted in situ keratomileusis [LASIK]).

One technology for direct measurement instead of estimating the posterior corneal curvature, called Total Keratometry (TK), is integrated in the IOLMaster 700 (Carl Zeiss Meditec AG, Jena, Germany).^{12} TK is a new keratometry value combining telecentric three-zone keratometry and swept-source optical coherence tomography (OCT) technology to determine the anterior and posterior corneal surface.^{13} Compared to standard keratometry, TK additionally considers corneal thickness and posterior corneal curvature. This can be advantageous for certain patients who may benefit from more accurate information about their total corneal power (eg, in astigmatic or post-LASIK eyes).^{4–8,14,15}

TK measures the refractive power of the cornea expressed in a toric model, consisting of three values (TK1, TK2, and Tα). TK is compatible with keratometry data for normal eyes, allowing TK values to be included in classic IOL calculation formulas. Additionally, existing optimized IOL constants can still be used.^{16} However, restrictions apply in cases where IOL calculation formulas are used that incorporate a specific model or nomogram to consider the posterior corneal surface (eg, in the Barrett Toric Calculator). In these formulas, the implementation of TK values would lead to overcorrection because the posterior corneal surface will be considered twice. To avoid this, Graham Barrett developed two new IOL power calculation formulas, the Barrett TK Universal II (for non-toric IOLs) and the Barrett TK Toric (for toric IOLs), both considering TK measurements from the IOLMaster 700.

The objective of this study was to evaluate and compare the prediction accuracy of the residual refraction in astigmatic eyes using standard keratometry and the new TK measurement values. For calculations including TK data, TK was applied to the Haigis formula and the two new Barrett formulas (Barrett TK Universal II and Barrett TK Toric).

### Patients and Methods

This post-hoc analysis of study data was based on a prospective study performed at two German clinics (AugenCentrum Rosenheim; AAZ Nürnberg) between July 2016 and January 2018. The study was approved by the local ethics committee and performed in accordance with the standard ISO 14155^{17} and the tenets of the Declaration of Helsinki. All patients provided written informed consent before enrollment.

The study population consisted of 145 patients receiving standard cataract or refractive lens exchange (145 eyes) who had already undergone uneventful phacoemulsification and implantation of CT Asphina 409M/MP IOLs (Carl Zeiss Meditec AG). Additional inclusion criteria were the availability of one reliable (quality check “green”) preoperative IOLMaster 700 measurement and the documentation of target refraction and IOL power calculation, clear ocular media, an expected postoperative corrected distance visual acuity (CDVA) of 20/30 or better, and a corneal astigmatism (keratometry) of 0.75 D or greater confirmed by the IOLMaster 700. Exclusion criteria were previous ocular surgery (except cataract or refractive lens exchange), poor tear film, ocular diseases or opacities that might impair vision, active ocular infection or inflammation, and the physical inability to be positioned at the slit lamp or study device (eg, head tremor).

The study examinations were performed at least 6 weeks after IOL implantation and included optical biometry (IOLMaster 700) and subjective refraction. Patients were asked to remove their contact lenses at least 2 weeks (rigid contact lens) or 1 day (soft contact lens) before the postoperative visit.

For the explorative analysis, TK and standard keratometry use outcomes were calculated at Carl Zeiss Meditec AG based on IOLMaster 700 raw data using the same algorithms as on the IOLMaster 700 application software version 1.70. The absolute prediction error (APE) of SE and cylinder based on keratometry and TK data was calculated as the difference between the actual postoperative refraction of the patient and the refractive error predicted by the Haigis and Barrett formulas. The Haigis-T (spherical component) and the Barrett Universal II (for TK data: Barrett TK Universal II) formulas were applied for APE calculations of SE, whereas the Haigis-T formula and the Barrett Toric Calculator (for TK data: Barrett TK Toric formula) were used for APE calculations of cylinder.

#### Statistical Analysis

Explorative data analysis was performed using SPSS Statistics software (version 24; IBM Corporation, Armonk, NY). The nature of retrospective post-hoc analyses does not consider sample size calculations. For the sample size calculation of the underlying study, the aim was to demonstrate non-inferiority of a calculation method using a 0.25 D acceptance limit for differences in APE between the different methods. In total, 144 eyes were required for a risk of 0.05 and a test power of 0.80. To compensate for possible dropouts, 157 eyes were included in the study. For the current post-hoc analysis, the data of 145 eyes were finally available. Descriptive statistics including frequency (percent), mean, standard deviation, median, and range of continuous data were applied. The difference in APE between standard keratometry and TK (standard keratometry minus TK) was obtained in all cases and analysis of differences was performed using the Bland–Altman plot method.^{18} The 95% limits of agreement were estimated by mean difference ± 1.96 × standard deviation of the differences, which provides an interval within which 95% of the differences between measurements are expected to lie. One-sided 95% confidence intervals for the mean of differences between keratometry and TK were determined. Considering the large sample size, the mean of the differences was assumed to be asymptotically normally distributed (central limit theorem) and confidence intervals were calculated using parametric methods.

### Results

A total of 145 eyes of 145 patients were included in the study. **Table 1** summarizes the clinical characteristics and implanted IOLs of the study population.

Table 1: Patient Demographics |

#### APE in SE Calculated With Haigis-T Formula

Descriptive statistics of APE in SE calculated with the Haigis-T formula based on standard keratometry and TK values are shown in **Table 1**. The APE from TK data showed a slight trend toward higher frequencies in the lower error ranges (**Figure 1**). Overall, 26.2% (n = 38) showed an APE of 0.50 D or greater for standard keratometry or TK calculations; in 65.8% (n = 25) of these cases, APE from TK was lower than from keratometry data. A pairwise comparison of APE values of these cases (APE from standard keratometry or TK 0.50 D or greater) is shown in **Figure 2A**. The spots in the diagram were predominantly distributed below the line of identity (same APE from keratometry and TK), meaning that APE from standard keratometry data were higher than from TK data for these patients. Descriptive statistics of differences between standard keratometry and TK are summarized in **Table 2**. The mean difference was positive, indicating that the APE calculated from standard keratometry data tended toward higher values compared to TK data (**Figure AA**, available in the online version of this article). This was confirmed by the limits of agreement (95%) of the Bland–Altman plot showing a positive shift of the ΔD values (**Table 2**, **Figure BA**, available in the online version of this article). The one-sided 95% confidence interval for the mean of these differences was (−0.004, infinity), demonstrating that the difference of APE between standard keratometry and TK data was higher than −0.004 D in 95% of the samples (ie, APE from standard keratometry data was predominantly equal to or greater than APE from TK data).

Figure 1. Cumulative percentage of eyes within the specified range of absolute prediction error (APE) in spherical equivalent (SE) (diopters [D]) for the different formulas. |

Table 2: Differences of APE (D) in SE and CYL Between K and TK (K − TK) Using Haigis-T and Barrett Formulas |

#### APE in SE Calculated With Barrett Universal II and Barrett TK Universal II Formulas

Descriptive statistics of APE in SE calculated with the Barrett Universal II (using standard keratometry values) and the Barrett TK Universal II (using TK values) formulas are shown in **Table 1**. As shown in **Figure 1**, APE from TK data marginally tended toward higher frequencies in the lower error ranges. Overall, 17.9% (n = 26) showed an APE of 0.50 D or greater for keratometry or TK calculations; in 73.1% (n = 19) of these cases, APE from TK was lower than from standard keratometry data. The pairwise comparison of APE outcomes of these cases (APE from standard keratometry and TK 0.50 D or greater) is shown in **Figure 2B**. Descriptive statistics of differences between standard keratometry and TK are summarized in **Table 2** and **Figure AB**. The APE calculated from standard keratometry data tended toward higher values compared to TK (**Table 2**, **Figure BB**) and the one-sided 95% confidence interval for the mean of these differences was 0.0005 to infinity.

#### APE in Cylinder Calculated With Haigis-T Formula

Descriptive statistics of the APE in cylinder calculated with the Haigis-T formula based on standard keratometry and TK values are summarized in **Table 3**. The distribution of data (**Figure 3**) showed a higher number of cases within ±0.50, ±0.75, and ±1.00 D of APE taking into account TK data. In total, 60.7% (n = 88) of cases showed an APE of 0.50 D or greater for standard keratometry and TK calculations; in 83.0% (n = 73) of these cases, APE from TK was lower compared to keratometry. **Figure 2C** shows a pairwise comparison of APE values of these cases (APE from keratometry and TK 0.50 D or greater). The mean difference between keratometry and TK calculations was positive (**Table 3**, **Figure AA**) and the limits of agreement of the Bland–Altman plot (**Table 3**, **Figure BC**) also showed a positive shift of the data distribution. The one-sided 95% confidence interval for the mean of these differences was 0.0791 to infinity.

Table 3: APE (D) in CYL Using Haigis-T and Barrett Toric Formulas Based on K and TK Values |

Figure 3. Cumulative percentage of eyes within the specified range of absolute prediction error (APE) in cylinder (CYL) (diopters [D]) for the different formulas. |

#### APE in Cylinder Calculated With Barrett TK Toric Formula and Barrett Toric Calculator

Descriptive statistics of the APE in cylinder calculated with the Barrett Toric Calculator (using standard keratometry values) and the Barrett TK Toric formula (using TK values) are shown in **Table 3**. The distribution of data (**Figure 3**) showed a higher number of cases within ±0.50, ±0.75, and ±1.00 D of APE taking into account TK data. In total, 40.7% (n = 59) of cases showed an APE of 0.50 D or greater for standard keratometry and TK calculations; in 69.5% (n = 41) of these cases, APE from TK was lower compared to standard keratometry. **Figure 2D** shows the pairwise comparison of APE values of these cases (APE from standard keratometry and TK 0.50 D or greater). The mean difference between standard keratometry and TK calculations was positive (**Table 3**, **Figure AB**) and the limits of agreement of the Bland–Altman plot (**Table 3**, **Figure BD**) showed a positive shift of the data distribution. The one-sided 95% confidence interval for the mean of these differences was −0.0002 to infinity.

### Discussion

Today, standard keratometry relies purely on measurements of the anterior corneal surface and determining total corneal power is performed by assuming a fixed ratio of the anterior and posterior curvature.^{3} However, the anterior and posterior curvature and the corneal thickness contribute to the total refractive power of the human cornea. Previous studies showed that ignoring the posterior curvature of the cornea could lead to significant overcorrection or undercorrection.^{4–8}

TK is now integrated into the IOLMaster 700.^{12} TK is based on actual measurements of the total cornea, which may be particularly advantageous for certain patients who may benefit from a more accurate information about their total corneal power (eg, in astigmatic or post-LASIK eyes).^{4–8,14,15}

Our results showed distinct trends after application of standard keratometry and TK data to the formulas Haigis-T, Barrett Universal II/Barrett TK Universal II, Barrett TK Toric, and the Barrett Toric Calculator. Overall, descriptive statistics showed a smaller distribution of APE for SE and cylinder when TK data were used instead of standard keratometry data. Consequently, retrospective calculations with standard keratometry parameters individually led to higher deviations from subjective refraction than calculations with TK. However, these individual maximum values may have resulted from outliers. In total, small APE for SE and cylinder from TK data were more frequent than from standard keratometry. Additionally, calculation of the differences of APE between standard keratometry and TK data confirmed more accurate results of TK, especially for cylinder outcomes of the Haigis-T formula. For explorative statistical analysis, the position of the mean of the differences in APE of standard keratometry and TK data was estimated at a significance level of 5%. For APE of SE using the Barrett Universal II and Barrett TK Universal II formulas, and for APE of cylinder using the Haigis-T formula, confidence intervals were higher than zero, demonstrating that in 95% of cases TK would in average result in a reduction of APE compared to keratometry.

Several authors compared the astigmatic prediction errors associated with different calculation methods and the effect of posterior corneal astigmatism on IOL power calculation.^{2,5–8,10,11,19} By using an industry-based calculator for toric lenses considering anterior keratometry values only, Kern et al.^{7} found a statistically significant postoperative undercorrection for SE and cylinder in all 64 eyes. The predicted postoperative refraction and toric lens power values were evaluated and compared after postoperative recalculation using the Barrett Toric calculator. The authors concluded that the prediction of postoperative refractive outcome can be improved by appropriate adjustment methods that take the corneal posterior surface into account.^{7} This was also confirmed by Ferreira et al.,^{19} who compared the prediction errors in residual astigmatism associated with several new calculation methods for toric IOLs (considering total corneal astigmatism) with the refractive results of a standard IOL calculator (considering only information of the anterior corneal surface). Among all evaluated methods, the mean APE in predicted residual astigmatism was highest using the standard IOL calculator (0.64 ± 0.38 D). whereas the Barrett Toric calculator yielded the lowest APE (mean 0.30 ± 0.27 D; *P* < .001).^{18}

In 2015, Abulafia et al.^{10} compared the error in predicted residual astigmatism for different corneal measuring devices and several methods of calculation. They also evaluated two methods that take into account the effect of posterior corneal astigmatism (Baylor nomogram and Barrett toric calculator) and both methods achieved lower centroid errors in predicted residual astigmatism (range: 0.21 to 0.26 D and 0.01 to 0.16 D, respectively) when all measuring devices were applied.^{10} These differences were significant compared with the Alcon and Holladay toric calculators.^{10} After toric IOL implantation, another case series showed that the corneal astigmatism prediction errors with devices that measure anterior corneal astigmatism only were 0.50 to 0.60 D in with-the-rule eyes and 0.20 to 0.30 D in against-the-rule eyes, showing the effect of posterior corneal astigmatism.^{11} To further improve refractive astigmatic outcomes after toric IOL implantation, Reitblat et al.^{8} proposed a method of combining posterior tomography measured by the Scheimpflug camera with anterior corneal astigmatism measurements by an optical low-coherence reflectometry device using vector summation.

Overall, taking posterior corneal astigmatism into consideration reduced the mean centroid simulated residual astigmatism from 0.47 D (anterior keratometry) to 0.22 D (vector analysis).^{8} However, combining the anterior and posterior inputs provided by different devices for total corneal power estimation may not be the ideal option. In contrast, this issue is obsolete by using TK, which combines the acknowledged anterior keratometry and simultaneously completes it with the missing information of the posterior surface within the same platform based on unchanged swept-source OCT technology already available and used in the IOLMaster 700.

A particular advantage of the new TK technology may be expected in IOL power calculation of unconventional cases. Prospective studies involving more eyes and different IOL models are needed to further investigate the accuracy of the new TK technology in different subgroups.

Our results indicate that instead of using standard keratometry in IOL power calculation, a higher prediction accuracy can be expected by applying TK values along with the Haigis formula and the two newly developed TK formulas.

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Patient Demographics

Patients/eyes (n) | 145/145 |

Right/left (%) | 42.1/57.9 |

Male/female (%) | 35.2/64.8 |

Age (y) | |

Mean ± SD | 73.17 ± 7.99 |

Median (range) | 74 (49 to 89) |

CDVA (logMAR) | |

Mean ± SD | 0.01 ± 0.06 |

Median (range) | 0.00 (−0.10 to 0.15) |

AL (mm) | |

Mean ± SD | 23.38 ± 1.25 |

Median (range) | 23.26 (20.59 to 27.38) |

ACD (mm) | |

Mean ± SD | 3.07 ± 0.36 |

Median (range) | 3.02 (2.31 to 3.93) |

LT (mm) | |

Mean ± SD | 4.58 ± 0.43 |

Median (range) | 4.61 (3.60 to 5.63) |

Average K (mm) | |

Mean ± SD | 7.68 ± 0.27 |

Median (range) | 7.71 (6.90 to 8.58) |

Cylinder (D) | |

Mean ± SD | 1.23 ± 0.56 |

Median (range) | 1.00 (0.75 to 4.25) |

Target refraction SE (D) | |

Mean ± SD | −0.35 ± 0.74 |

Median (range) | −0.11 (−3.30 to 0.57) |

IOL SE power | |

Mean ± SD | 20.92 ± 3.20 |

Median (range) | 21.00 (10.00 to 28.50) |

Differences of APE (D) in SE and CYL Between K and TK (K − TK) Using Haigis-T and Barrett Formulas

Mean | 0.011 | 0.016 | 0.103 | 0.020 |

SD | 0.107 | 0.113 | 0.173 | 0.148 |

Median | 0.006 | 0.012 | 0.136 | 0.048 |

Minimum | −0.300 | −0.220 | −0.350 | −0.410 |

Maximum | 0.430 | 0.430 | 0.480 | 0.350 |

95% limit of agreement | −0.119 to 0.221 | −0.206 to 0.335 | −0.237 to 0.513 | −0.269 to 0.437 |

APE (D) in CYL Using Haigis-T and Barrett Toric Formulas Based on K and TK Values

Mean | 0.587 | 0.484 | 0.434 | 0.413 |

SD | 0.309 | 0.264 | 0.253 | 0.231 |

Median | 0.549 | 0.456 | 0.398 | 0.377 |

Minimum | 0.003 | 0.000 | 0.026 | 0.030 |

Maximum | 1.587 | 1.387 | 1.436 | 1.226 |