Measured Corneal Astigmatism Versus Pseudophakic Predicted Refractive Astigmatism in Cataract Surgery Candidates


  • Total corneal astigmatism (TCA) measurements and predicted refractive astigmatism by the Barrett toric calculator are not interchangeable.

  • TCA alone may not serve as an adequate reference for deciding the need for toric intraocular lens implantation.


To compare standard and total corneal astigmatism measurements to the predicted pseudophakic (nontoric) refractive astigmatism in candidates for cataract surgery.


A retrospective, cross-sectional study.


A single-center analysis of consecutive eyes measured with a swept-source optical coherence tomography biometer at a large tertiary medical center between February 2018 and June 2020. Corneal astigmatism was calculated based on standard keratometry astigmatism (KA), total corneal astigmatism (TCA), and predicted refractive astigmatism (PRA) for a monofocal nontoric intraocular lens (IOL) implantation calculated by the Barrett toric calculator using the predicted posterior corneal astigmatism (PRA (Predicted-PCA) ) and the measured posterior corneal astigmatism (PRA (Measured-PCA) ) options. Separate analyses were performed for each eye.


Ophthalmology Department, Shaare Zedek Medical Center, Jerusalem, Israel.


In total, 8152 eyes of 5320 patients (4221 right eyes [OD] and 3931 left eyes [OS], mean age 70.6±12.2 years, 54.2% females) were included in the study. The mean vector values (centroid) for KA, TCA, PRA (Predicted-PCA) , and PRA (Measured-PCA) were 0.07 diopters [D] at 19.5°, 0.27 D at 7.5°, 0.44 D at 2.9°, and 0.43 D at 179.3°, respectively ( P < .01), for OD and 0.02 D at 150.3°, 0.23 D at 169.7°, 0.40 D at 179.4°, and 0.42 D at 169.5°, respectively ( P < .01), for OS. More than 73% of eyes had a PRA >0.5 D.


Standard and total corneal astigmatism measurements differ significantly from the PRA by the Barrett toric calculator. The PRA, rather than the KA or TCA, should be used as the reference guide for astigmatism correction with toric IOL implantation.

C orneal astigmatism is a common condition in the cataract population. Wasser and associates reported that almost 60% of their cataract patients had total corneal astigmatism (TCA) of 0.75 diopters (D) or higher. Minimizing postoperative refractive astigmatism following cataract surgery is essential to achieve spectacle independence. Residual astigmatism greater than 0.75 D can reduce visual acuity to 20/25 or less and increase the likelihood that spectacle correction will be required. Our objective was to determine the impact of different parameters when used as a reference guide for astigmatism correction with toric IOL implantation.

In the past, standard keratometric astigmatism (KA) has been used as the reference for assessing the need for astigmatism correction during cataract surgery. In 2012, Koch and associates found that ignoring the posterior corneal astigmatism (PCA) may lead to inaccurate estimation of the total (ie, anterior and posterior) measured corneal astigmatism. Although TCA is more accurate than KA for assessing the need for and the extent of astigmatism correction during cataract surgery, the postoperative predicted refractive astigmatism (PRA) following a nontoric IOL implantation takes into account not only the posterior astigmatism but also the predicted corneal surgically induced astigmatism (SIA) and, depending on the method of prediction, other factors, such as the physiological intraocular lens (IOL) tilt. ,

In the current study, we evaluated the PRA values, determined by the Barrett toric calculator in 2 separate modes in a large cataract surgery database: (1) PRA with the “predicted PCA” (PRA (Predicted-PCA) ) and (2) PRA with the “measured PCA” (PRA (Measured-PCA) ), and compared them to the KA and TCA measurements.


This study is a retrospective single-center cross-sectional analysis of consecutive eyes whose ocular biometric parameters were measured with a swept-source optical coherence tomography system (SS-OCT) device at the Department of Ophthalmology of Shaare Zedek Medical Center in Jerusalem between February 2018 and June 2020. Inclusion criteria were age ≥18 years, eyes with no previous cataract or refractive surgery, and biometric measurements with complete and quality data, as defined by successful repeat measurements of each parameter. All patients who were aligned with the inclusion criteria were included in the study and no further exclusion criteria were applied. A single measurement was randomly chosen in subjects with more than 1 successful measurement. This study conformed to the Declaration of Helsinki and was approved by the Shaare Zedek Medical Center Institutional Review Board.

The IOLMaster 700 (Carl Zeiss, Meditec, software version biometry device was used throughout this study. Standard keratometry (K) was calculated by 1000 × (1.3375 – 1)/R anterior . Mean keratometry was defined by (K steep +K flat )/2. Posterior corneal power (PK) was calculated by 1000 × (−0.04)/R posterior . Standard KA was calculated as K steep – K flat . TCA was calculated as TK steep – TK flat . PCA was calculated as posterior K steep – posterior K flat. The features of the SS-OCT standard (K) and total keratometry (TK) measurements are described in detail elsewhere.

The predicted postoperative residual astigmatism for a monofocal (SN60WF, lens factor =1.88) nontoric IOL implantation was calculated with the Barrett toric calculator (version 2.0, access date January 1, 2022) in 2 separate modes: (1) PRA (Predicted-PCA) in which the PRA with the “predicted-PCA” mode was chosen using standard Ks with a corneal SIA of 0.10 D at 0/180°, and (2) PRA (Measured-PCA) in which the PRA with the “measured-PCA” mode was chosen using standard Ks, PK, and a corneal SIA of 0.10 D at 0/180°.


Mean vector (centroid) values were calculated for KA, TCA, PCA, PRA (Predicted-PCA) , and PRA (Measured-PCA) with the R software, based on vector analysis as described by Holladay and associates. Absolute magnitude astigmatism was compared between the various groups. Analyses were performed separately for each eye, except when direct comparisons were done between the right and left eyes. Data are graphically presented by means of double-angle plots.


The Shapiro-Wilk test was used for univariant normality analysis. The distribution of the estimated centroid should follow a bivariate Normal under reasonable sample sizes (n > 40) because of the central limit theorem. A permutation-based multivariate analysis of variance was therefore applied for comparing the centroids of the 4 groups, followed by a Hotelling T 2 post hoc analysis of the pairwise post hoc analysis to identify significantly different pairs. The 95th percentile of observation distance from the median was calculated by Bootstrap and used as a distance threshold. Convex polygons containing the points that are closer to the median than the threshold were included (the convex polygon is the smallest convex polygon containing a set of measurements). The total variance was calculated as the sum of partial variances of x and y , and the total SD of data as the square root of the total variance.

Nonparametric analysis of variance, the Friedman test for paired groups, and the Kruskal-Wallis test for nonpaired groups were used for comparing the astigmatism magnitudes, followed by post hoc analysis with a pairwise Wilcoxon signed rank test or pairwise Wilcoxon rank sum tests, respectively. The percentage of eyes with an astigmatism magnitude >0.50 were compared by the McNemar test. P values were adjusted with the Holm-Bonferroni correction method for multiple tests. The significance level (alpha) was set to 0.05. The analysis was carried out with the R software (A Language and Environment for Statistical Computing, ). Graphics were created with ggplot2.


A total of 8152 eyes of 5320 consecutive patients (4221 right eyes [OD] and 3931 left eyes [OS]) were included in this study. The patients’ demographics and biometric data are presented in Tables 1 and 2 , respectively. The mean astigmatism magnitude of the different groups ranged between 1.0 and 1.10 D, and although the differences were small, they still reached a level of significance, except for KA vs PRA (Predicted-PCA) , OD: P = .47; KA vs PRA (Predicted-PCA) , OS: P = .37; and KA vs PRA (Measured-PCA) , OS: P = .08 ( Table 3 ). Figure 1 displays the distribution of the astigmatism magnitude in the study population. The percentages of eyes with an astigmatism magnitude >0.5 D were greater for both eyes in the TCA group compared with the KA, PRA (Predicted-PCA) , and PRA (Measured-PCA) groups, P < .01.


Patient Demographics

Parameter Total Right Eye Left Eye
Eyes, n (patients, n) 8152 (5320) 4221 3931
Age, y, mean ± SD (range) 70.60 ± 12.19 (18-99) 70.22 ±12.24 (18-99) 70.81 ± 11.32 (18-99)
Male 2437 (45.81%) 1913 (45.32%) 1785 (45.41%)
Female 2883 (54.19%) 2308 (54.68%) 2146 (54.59%)


Biometric Parameters

Parameter OD Mean ± SD (Range) OS Mean ± SD (Range)
Axial length (mm) 23.92 ± 1.54 (19.37, 34.02) 23.92 ± 1.57 (19.25, 34.00)
K flat (D) 43.52 ± 1.63 (37.28, 50.44) 43.59 ± 1.66 (37.81, 51.17)
K steep (D) 44.56 ± 1.72 (39.22, 53.30) 44.61 ± 1.78 (39.08, 55.94)
Mean keratometry (D) 44.04 ± 1.62 (38.96, 51.78) 44.10 ± 1.67 (38.86, 53.56)
TK flat (D) 43.55 ± 1.64 (37.47, 50.58) 43.63 ± 1.68 (37.94, 51.19)
TK steep (D) 44.65 ± 1.72 (39.40, 53.09) 44.71 ± 1.78 (39.13, 55.74)
Mean total keratometry (D) 44.10 ± 1.63 (38.89, 51.55) 44.17 ± 1.68 (38.77, 53.33)
Posterior K flat (D) –5.73 ± 0.25 (–7.00, –4.81) –5.73 ± 0.25 (–7.11, –4.86)
Posterior K steep (D) –5.98 ± 0.28 (–7.47, –5.11) –5.99 ± 0.28 (–7.77, –5.13)
Mean posterior keratometry (D) –5.86 ± 0.25 (–7.21, –5.02) –5.86 ± 0.26 (–7.44, –4.99)
Anterior chamber depth (mm) 3.17 ± 0.42 (1.83, 5.28) 3.17 ± 0.42 (1.78, 4.94)
Lens thickness (mm) 4.50 ± 0.46 (2.52, 6.55) 4.51 ± 0.46 (2.54, 6.09)
Central corneal thickness (mm) 0.54 ± 0.04 (0.41, 0.67) 0.54 ± 0.04 (0.42, 0.67)
White-to-white (mm) 11.92 ± 0.43 (10.19, 13.56) 11.93 ± 0.44 (10.34, 13.44)

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Sep 11, 2022 | Posted by in OPHTHALMOLOGY | Comments Off on Measured Corneal Astigmatism Versus Pseudophakic Predicted Refractive Astigmatism in Cataract Surgery Candidates
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