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Cornea  |   January 2015
Anterior Surface–Based Keratometry Compared With Scheimpflug Tomography–Based Total Corneal Astigmatism
Author Notes
  • Department of Ophthalmology, Goethe-University, Frankfurt am Main, Germany 
  • Correspondence: Thomas Kohnen, Department of Ophthalmology, Goethe-University Frankfurt am Main, Theodor-Stern-Kai 7, 60590 Frankfurt am Main, Germany; kohnen@em.uni-frankfurt.de
Investigative Ophthalmology & Visual Science January 2015, Vol.56, 291-298. doi:10.1167/iovs.14-15659
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      Bastian Tonn, Oliver Klaus Klaproth, Thomas Kohnen; Anterior Surface–Based Keratometry Compared With Scheimpflug Tomography–Based Total Corneal Astigmatism. Invest. Ophthalmol. Vis. Sci. 2015;56(1):291-298. doi: 10.1167/iovs.14-15659.

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      © ARVO (1962-2015); The Authors (2016-present)

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Abstract

Purpose.: Description of total corneal refractive power (TCRP) astigmatism by ray tracing using a Scheimpflug tomographer.

Methods.: Analysis of Scheimpflug tomography measurements to determine 3-mm-zone TCRP astigmatism (CATCRP) by ray tracing calculations, astigmatism in 15°-zone from simulated keratometry (CASim-K), anterior-surface astigmatism (CAant), and posterior-surface astigmatism (CApost). An analysis of changes with age was performed. The error produced by estimating CATCRP using CASim-K was calculated through vector analyses. The percentages of steep meridian aligned vertically, obliquely, and horizontally of CAant and CApost were calculated.

Results.: A total of 3818 healthy, previously unoperated eyes were analyzed. The mean magnitude of CApost was −0.33 diopter (D). A vertically aligned steep meridian (60° to 120°) was found in 71.2% of eyes for CAant and in 88.8% for CApost. With increasing age, the occurrence of steep meridian aligned horizontally in CAant increased from 9.1% (age 20–29 years) to 31.8% (70–79 years), while vertical alignment decreased from 77.4% to 48.1%. Alignment of CApost mostly remained vertical (90.9%–80.7%). When CAant is vertical, CApost is vertical in 97% and CASim-K overestimates total corneal astigmatism (mean 0.11 ± 0.22 D). When CAant is horizontal, 18% of CApost is horizontal and CASim-K underestimates (mean 0.26 ± 0.31 D) total corneal astigmatism. The mean vector difference between CATCRP and CASim-K was 0.18 at 178° and exceeded 0.50 D in 9% of eyes.

Conclusions.: Total corneal astigmatism is overestimated by CASim-K in eyes with with-the-rule astigmatism and cannot be predicted safely in eyes that do not have with-the-rule astigmatism by anterior measurements only.

Introduction
Anterior curvature, as well as corneal thickness and posterior curvature, contribute to total corneal astigmatism. Today, precise estimation of astigmatism is a key factor in the outcome of refractive surgical corrections and cataract surgery (e.g., before lens implantation). Devices using anterior measurements only, such as keratometry and autokeratometry, include the contribution of the cornea's thickness and posterior curvature through an empiric index (“keratometric-index”) when calculating total corneal power and do not take into account its individual shape and thickness. Scheimpflug tomographers provide a map of the anterior chamber and therefore a more accurate model of the cornea, its thickness, and posterior surface. Current Scheimpflug tomographers assess total corneal power with the use of ray tracing, a technique that calculates the individual refraction of rays depending on the model of the cornea's surface and its thickness. In accordance with Snell's law, incoming parallel rays are refracted through the anterior and posterior corneal surface with real refraction index numbers (1 for air, 1.376 for cornea, 1.336 for aqueous), which means that refracted rays, instead of parallel rays, reach the posterior corneal surface. 
Several devices, such as Purkinje images, scanning-slit topography,16 Scheimpflug imaging using vector summation, optical coherence tomography, ray tracing with a dual Scheimpflug analyzer merged with Placido disk (Galilei dual Scheimpflug analyzer; Ziemer Group, Port, Switzerland) and a Scheimpflug tomographer (Pentacam HR; Oculus, Wetzlar, Germany) have been used to measure the influence of posterior astigmatism on total corneal astigmatism.713 In addition, the alignment of the steep meridian of astigmatism on the anterior and posterior surface, along with the effects of aging, has been analyzed. The steep meridian of anterior astigmatism tends to change from vertical alignment to horizontal alignment, whereas the steep meridian of posterior astigmatism seems to remain vertical.10,11,13 In addition, Koch et al.11 found a moderate correlation between the magnitude of anterior and posterior astigmatism, when the steep meridian is aligned vertically on the anterior surface. With an increasing difference between anterior and posterior alignment, the difference between total corneal astigmatism measured via anterior measurements and total corneal astigmatism calculated through ray tracing increased. 
To our knowledge, our study is the first to calculate the distribution of the alignment of posterior astigmatism and the mean estimation error depending on alignment of anterior astigmatism. Furthermore, this study has the highest case number evaluating posterior astigmatism. The purpose of our study was to describe total corneal refractive power (TCRP) astigmatism by ray tracing using a rotating Scheimpflug tomographer (Pentacam HR; Oculus) and the factors that may lead to false calculation of total corneal astigmatism by using anterior curvature measurements only. 
Patients and Methods
Institutional review board approval was obtained from the Frankfurt Ethical Commission and the tenets of the declaration of Helsinki were followed throughout the study. The study retrospectively reviewed all the Scheimpflug images taken in the Department of Ophthalmology, Goethe-University Frankfurt am Main, from March 2010 to June 2013. The inclusion criterion meant only patients with good-quality Scheimpflug scans (labeled “OK” by the Pentacam in the “Examination Quality Specification”) were included. Each scan had parameters that met the manufacturer's specifications and valid data of 95% or more. The exclusion criteria were as follows: patients who had been clinically classified with corneal diseases (e.g., keratoconus), matching Amsler topographic keratoconus classification as displayed by the Pentacam, an astigmatism in the 15°-zone from simulated keratometry (CASim-K) less than 39 diopters (D) or greater than 49 D, age younger than 20 or older than 79, and previous corneal surgery. 
Measurements
The Pentacam uses a slit illumination system and a rotating camera, which takes pictures in accordance with the Scheimpflug principle. In doing so, it creates a completely focused image of the anterior eye segment. The sectional images are saved and a three-dimensional model of the entire anterior eye segment is extrapolated from these images. Eye motions during the scan are detected by the second iris camera and corrected mathematically. Ray tracing is a technique that can be used to simulate the optical path refracted through the anterior corneal surface, corneal stroma, and the posterior corneal surface to calculate TCRP. Previous studies showed that TCRP, anterior and posterior corneal astigmatism values, were repeatable and reproducible.1416 The Scheimpflug tomographer was calibrated with the test tool by the company before the first measurement used in this study. 
Parameters
The CATCRP is defined in this trial as the astigmatism value derived from TCRP in the 3-mm zone. It is calculated by ray tracing according to Snell's law through the anterior and posterior corneal surfaces using the refractive index numbers 1 for air, 1.376 for the cornea, and 1.336 for aqueous humor. The 3-mm zone was chosen to closely match the standard 15° zone of a keratometric analysis, CASim-K
The CASim-K is defined as the astigmatism value from simulated keratometry in the 15° zone, which equals approximately the 3-mm zone of the anterior surface. We multiplied the curvatures of the steep radius (Rs) and flat radius (Rf) with (ns − 1), where ns is the standard refractive index of 1.3375 and 1 is the refractive index number of air, to calculate the steep and flat K, respectively. The CASim-K is the difference between the steep and flat K; the meridian is the steep CASim-K meridian, and CASim-K represents the anterior corneal measurement only. 
The CAant is defined as the astigmatism value solely from the anterior corneal surface. The CAant is calculated from CASim-K by multiplying with (nc − 1)/ (ns − 1), where nc is the refractive index number of the cornea (1.376). 
The CApost is defined as the astigmatism value of the posterior corneal surface evaluated by the Pentacam in the 15° zone, equal to the 3-mm zone. It is calculated using the curvatures of the Rs and Rf of the posterior astigmatism and the refractive index of the cornea and aqueous humor: (nanc)/(Rs) − (nanc)/(Rf). The meridian is the steep meridian. 
Data Analysis
We assessed the mean magnitude, SD, and range of corneal astigmatism provided by CATCRP, CASim-K, CAant, and CApost. The percentage of eyes that had a magnitude up to 0.25, 0.50, 0.75, and 1.00 D was determined. 
The correlation of magnitude between anterior and posterior astigmatism depending on the alignment of astigmatism on the anterior surfaces was measured. Eyes with CASim-K steep meridian from 60° to less than 120° were classified as vertically aligned, from 30° to less than 60° and 120° to less than 150° as obliquely, and from 0° to less than 30° and 150° to less than 180° as horizontally. 
To describe the relationship between the alignment of astigmatism on the anterior and posterior surfaces, we divided the eyes into groups as described above. In addition, to perform an analysis of age-related change of alignment, eyes were separated into groups depending on age of the patients at their examination. We used vector analysis to create aggregate corneal astigmatism.17 
To calculate the estimation error by neglecting posterior astigmatism, the vector difference between CASim-K, representing anterior measurements only, and CATCRP as the gold standard was assessed using vector analysis.17 We evaluated the mean magnitude of the difference between CATCRP and CASim-K depending on age and the percentage of eyes that had a difference in magnitude up to 0.25, 0.5, 0.75, and 1.00 D. We calculated the percentage of eyes that had an absolute difference in magnitude between CATCRP and CASim-K that exceed 50% of CASim-K. The difference between the alignment of the steep meridian between CATCRP and CASim-K and eyes that had differences within 5° and 10° were obtained. We analyzed the differences between CATCRP and CASim-K and the differences between the alignment of the steep meridian on the anterior and posterior surfaces in relation to the alignment of the steep meridian on the anterior surface. The mean difference of magnitude between CATCRP and CASim-K when anterior astigmatism was aligned vertically and horizontally was calculated. 
Statistics
To determine the relationship between the differences in the steep meridian on anterior and posterior surfaces depending on the axes of anterior astigmatism, the differences between the axes CATCRP and CASim-K as a function of the axis of anterior astigmatism, the differences in the steep meridian on anterior and posterior surfaces depending on the axis of anterior astigmatism, the magnitude of astigmatism on the anterior and posterior corneal surfaces, and the differences in magnitude between CATCRP and CASim-K depending on the magnitude of CASim-K correlation analyses have been processed. Statistical analysis was performed using Excel for Mac (version 12.3.6; Microsoft, Inc., Redmond, WA, USA). 
Results
This study included 3818 eyes (1909 right, 1909 left) of 2233 patients in total. The mean age of the subjects was 47.5 ± 15.0 years (range, 20–79 years). The subgroups of eyes based on age at the time of their examination were as follows: 561 eyes from 20 to 29 years, 689 eyes from 30 to 39 years, 895 eyes from 40 to 49 years, 775 eyes from 50 to 59 years, 536 eyes 60 to 69 years, and 362 eyes from 70 to 79 years (Table 1). The mean magnitude of posterior corneal astigmatism of these eyes was −0.33 ± 0.18 D (range, 0.00 to −1.35 D) (Table 2). 
Table 1.
 
Aggregate Anterior and Posterior Corneal Astigmatism
Table 1.
 
Aggregate Anterior and Posterior Corneal Astigmatism
Age, y Eyes Mean ± SD, D
Anterior Cornea Posterior Cornea
20–29 561 1.13 ± 1.15 at 88.79° −0.33 ± 0.19 at 87.71°
30–39 680 0.85 ± 1.04 at 88.73° −0.28 ± 0.18 at 87.79°
40–49 895 0.94 ± 1.04 at 88.21° −0.29 ± 0.18 at 88.21°
50–59 775 0.89 ± 0.94 at 88.32° −0.30 ± 0.17 at 88.49°
60–69 536 0.54 ± 0.81 at 88.99° −0.23 ± 0.16 at 89.36°
70–79 362 0.21 ± 0.82 at 87.64° −0.21 ± 0.17 at 88.13°
Table 2
 
Corneal Astigmatism Magnitude, n = 3818
Table 2
 
Corneal Astigmatism Magnitude, n = 3818
Parameter Magnitude, D Percentage of Eyes
Mean ± SD Range ≤0.25 D ≤0.50 D ≤0.75 D ≤1.00 D
CATCRP 1.13 ± 0.89 0–7.2 26.4 60.0
CASim-K 1.15 ± 0.90 0–7.27 6.4 22.5 38.6 55.1
CAant 1.28 ± 1.01 0–8.10 5.3 19.0 33.2 49.0
CApost −0.33 ± 0.18 0 to −1.35 35.2 85.0 97.4 99.6
There were 2717 eyes (71.2%) that had a vertical alignment of the steep meridian on the anterior surface, whereas 3390 eyes (88.8%) had a vertical alignment on the posterior surface (Fig. 1). If anterior astigmatism was vertical, posterior alignment was vertical in 97%, oblique in 3%, and horizontal in 0%. With anterior oblique astigmatism, posterior astigmatism was vertical in 79%, oblique in 18%, and horizontal in 3%. In contrast, eyes with anterior horizontal astigmatism showed a vertical alignment of posterior astigmatism in only 59%, oblique alignment in 23%, and horizontal alignment in 18%. The difference between the axis of anterior and posterior astigmatism increased the more the axis of anterior astigmatism differed from the 90° meridian (r = 0.72) (Fig. 2a). Also, the difference in magnitude between CATCRP and CASim-K significantly increased the larger the difference in the location of the steep meridian between anterior and posterior corneal astigmatism (r = 0.62) (Fig. 3) was and therefore with increasing difference of the axis of anterior astigmatism from the 90° meridian (r = 0.48) (Fig. 2b). The mean difference between CATCRP and CASim-K was −0.11 ± 0.22 D when alignment of anterior astigmatism was vertical and +0.26 ± 0.31 D when horizontal. It increased from −0.10 ± 0.23 D in patients in their 20s to +0.10 ± 0.31 D in patients in their 70s (Table 3). 
Figure 1
 
Location of steep meridian on anterior and posterior corneal surfaces.
Figure 1
 
Location of steep meridian on anterior and posterior corneal surfaces.
Figure 2
 
Differences between anterior corneal steep meridian and posterior corneal steep meridian ([a] r = 0.72) and differences in magnitude between CATCRP and CASim-K ([b] r = 0.48) as a function of the anterior corneal steep meridian.
Figure 2
 
Differences between anterior corneal steep meridian and posterior corneal steep meridian ([a] r = 0.72) and differences in magnitude between CATCRP and CASim-K ([b] r = 0.48) as a function of the anterior corneal steep meridian.
Figure 3
 
Differences between anterior corneal steep meridian and posterior corneal steep meridian as a function of the differences in magnitude between CATCRP and CASim-K (r = 0.62). Eyes with anterior steep meridian aligned horizontally and posterior steep meridian aligned vertically are in black, other combinations of alignment are in gray.
Figure 3
 
Differences between anterior corneal steep meridian and posterior corneal steep meridian as a function of the differences in magnitude between CATCRP and CASim-K (r = 0.62). Eyes with anterior steep meridian aligned horizontally and posterior steep meridian aligned vertically are in black, other combinations of alignment are in gray.
Table 3
 
Over- and Underestimation of Total Corneal Astigmatism
Table 3
 
Over- and Underestimation of Total Corneal Astigmatism
Age, y Eyes Magnitude CATCRP – CASim-K, D
Mean ± SD Range
20–29 561 −0.10 ± 0.23 −0.94 to 1.53
30–39 680 −0.05 ± 0.25 −0.84 to 2.37
40–49 895 −0.06 ± 0.25 −0.84 to 1.82
50–59 775 −0.03 ± 0.27 −0.87 to 2.42
60–69 536 0.05 ± 0.31 −0.88 to 1.67
70–79 362 0.10 ± 0.31 −1.11 to 2.58
With increasing age, on the anterior corneal surface, vertical alignment of the steep meridian decreased from 77.4% (434 eyes) in the group of 20 to 29-year-old patients to 48.1% (174 eyes) in the group of 70 to 79-year-old patients, whereas the percentage of patients with horizontal alignment increased from 9.1% (51 eyes) to 31.8% (115 eyes) (Fig. 4a). However, on the posterior surface, there was only a marginal decrease of vertical alignment from 90.9% (510 eyes) to 80.7% (292 eyes) and increase of horizontal alignment (Fig. 4b). Anterior aggregate mean astigmatism decreased from 1.13 ± 1.15 D to 0.21 ± 0.82 D, while its alignment remained with-the-rule (WTR). On the posterior surface, there were only slight changes (Table 1). 
Figure 4
 
Percentage of eyes with vertical, horizontal, and oblique steep meridian in each decade on anterior corneal surface (a) and posterior corneal surface (b).
Figure 4
 
Percentage of eyes with vertical, horizontal, and oblique steep meridian in each decade on anterior corneal surface (a) and posterior corneal surface (b).
Correlation analysis between the magnitude of CAant and CApost showed strong (anterior alignment vertical r = 0.77) to moderate (anterior alignment oblique r = 0.50, anterior alignment horizontal r = 0.43) correlation (Fig. 5). 
Figure 5
 
Magnitude of astigmatism on the anterior corneal surface and posterior corneal surface grouped according to the orientation of the steep meridian on the anterior cornea. (a) vertical (r = 0.77); (b) oblique (r = 0.50); (c) horizontal (r = 0.41).
Figure 5
 
Magnitude of astigmatism on the anterior corneal surface and posterior corneal surface grouped according to the orientation of the steep meridian on the anterior cornea. (a) vertical (r = 0.77); (b) oblique (r = 0.50); (c) horizontal (r = 0.41).
The CATCRP aggregate mean astigmatism was measured 0.56 ± 0.89 D at 88.6° and 0.73 ± 0.90 D at 88.7° for CASim-K. The mean vector difference between CATCRP and CASim-K was 0.18 ± 0.19 D at 178.4°. A percentage of 54.7% (2665 eyes) had a vector difference within 0.25 D, 90.9% (3738 eyes) within 0.50 D, and 99.2% within 1.00 D (3816 eyes). 
The arithmetic mean of differences in magnitude was −0.03 ± 0.28 D (range, −1.11 to +2.58 D), with an absolute mean of 0.21 ± 0.19 D. Percentages of 71.2% (2720 eyes) and 94.2% (3596 eyes) had differences within ±0.25 D and ±0.50 D, respectively. The absolute difference between CATCRP and CASim-K exceeded 50% of CASim-K in 13.5% (Fig. 6). The correlation analyses between the difference of CATCRP and CASim-K and CASim-K showed no correlation. The mean difference in axis between CATCRP and CASim-K was 7.3° ± 11.4° (range, 0.0°–89.6°). Percentages of 62.3% (2377 eyes) and 79.9% (3049 eyes) had differences within ±5° and ±10°, respectively. 
Figure 6
 
Differences between CATCRP and CASim-K as a function of CASim-K. Differences that exceed 50% of CASim-K are in black.
Figure 6
 
Differences between CATCRP and CASim-K as a function of CASim-K. Differences that exceed 50% of CASim-K are in black.
Discussion
In our study, the mean magnitude of posterior corneal astigmatism was assessed −0.33 ± 0.18 D by a rotating Scheimpflug tomographer (Pentacam HR; Oculus). Most Scheimpflug tomographers, such as the Pentacam, use Snell's law and ray tracing technology to determine the total corneal power and total corneal astigmatism by calculating the individual refraction at the anterior surface, the corneal thickness, and posterior surface. Unlike these devices, manual and automated keratometers and Placido disk corneal topographers assume parallel rays refracted through the cornea. Previous studies showed that corneal power values assessed using Scheimpflug tomographers are repeatable and comparable.14 This study, to our knowledge, has the highest case number regarding posterior astigmatism, and is the first to describe the percentage of constellations between alignment of anterior and posterior astigmatism and constellations that lead to overestimation and underestimation with the mean magnitude of the estimation error. 
Vector analysis showed a mean estimation error for CASim-K of 0.18 ± 0.19 D at 178.4° and 9.1% of eyes had a mean vector difference between CATCRP and CASim-K of more than 0.50 D. In most cases, posterior curvature created against-the-rule (ATR) astigmatism, due to its negative corneal power and vertical alignment. Thus, the vector difference between CATCRP and CASim-K is located at 180°. With IOL selection based on CASim-K, 5.8% had an error of magnitude of more than 0.50 D and 20.1% had an alignment error of more than 10°. In 13.5%, the absolute difference between CATCRP and CASim-K was 50% or more of the measured CASim-K. Accordingly, CASim-K of 1.00 D or less, in particular, includes the risk of an astigmatism 50% smaller or higher than measured using only anterior measurements or of an astigmatism value that is measured with 0.00 D when evaluated with TCRP. 
The correlation between the magnitude of anterior and posterior corneal astigmatism was strong (r = 0.77) with anterior vertical alignment, and decreased to moderate the more the alignment shifted over from oblique (r = 0.50) to horizontal (r = 0.43). However, the magnitude of posterior astigmatism ranged from −1.35 to −0.01 D with anterior alignment vertical, −0.98 to 0.00 D with anterior alignment oblique and −1.11 to 0.00 D with a clinically important variability. These results suggest that an accurate determination of the magnitude of posterior astigmatism cannot be done by anterior measurements only. 
Furthermore, this study calculated the percentages of individual constellations of the alignment of astigmatism on the anterior and posterior surfaces, because the difference between CATCRP and CASim-K increased with increasing differences between their axes (Fig. 3). When the steep meridian on the anterior surface is aligned vertically, it creates WTR astigmatism, vertical alignment on the posterior surface produces ATR astigmatism, which has negative power and partly compensates the anterior astigmatism. A vertical alignment on the anterior surface was associated with a vertical posterior alignment in 97% and CASim-K overestimated total astigmatism by 0.11 D on average. In contrast, only 18% of posterior astigmatism was aligned horizontally, when anterior astigmatism was aligned horizontally, so that the posterior could partly compensate anterior astigmatism. In 59%, the posterior astigmatism was aligned vertically, contributing ATR to the ATR of the anterior surface. These percentages remained distributed constantly over age (not shown). Consequently, CASim-K underestimated total astigmatism by a mean of 0.26 D, when anterior astigmatism was aligned horizontally. This indicates that especially with an anterior horizontal alignment of astigmatism, it is questionable as to what the value of these measurements is and an analysis of the posterior astigmatism is suggested. We believe that due to the inclusion of the rather rare constellation that leads to underestimation, the keratometric refractive index tends to overestimate in most cases (namely when anterior alignment of astigmatism is vertical). 
The age analyses showed a vertical alignment that tended to shift to horizontal with increasing age. In contrast, the posterior alignment remained vertical. Therefore, posterior astigmatism partly compensates anterior astigmatism in younger patients but tends to increase ATR astigmatism in older patients. As a result, the risk of overestimation of total corneal astigmatism by the exclusive use of anterior measurements is higher in younger patients, whereas the risk of underestimation increases with increasing age (Table 3). 
The impact of posterior astigmatism is an issue that still attracts controversy when discussed. Although some authors state the hypothesis that accurate enough calculations can be provided by anterior measurements only, current studies show that ignoring posterior astigmatism can lead to miscalculation in certain cases, and further investigations are required.1820 Posterior astigmatism has been evaluated by different devices, such as Purkinje images, scanning-slit imaging, Scheimpflug imaging, and optical coherence tomography with a mean posterior astigmatism ranging from 0.26 to 0.78 D.1,3,68,10,11 In our study, the mean magnitude of posterior corneal astigmatism (−0.33 ± 0.18 D) is similar to other newer Scheimpflug analyses that ranged from −0.30 to −0.33 D (Table 4). However, Koch et al.11 and Ho et al.9 estimated the mean vector difference (0.22 D at 180°, 0.28 D at 177.2°, respectively, compared with 178.4°) and the occurrence of anterior vertical astigmatism (50.9%, 71.8%, respectively, compared with 71.2%) and posterior vertical astigmatism (86.6%, 96.1%, respectively, compared with 88.8%) with some differences. Therefore demonstrating the same tendencies as our values had, despite the use of different devices and methods (Table 4).9,11 These groups also analyzed the age-related changes of the steep meridian of anterior astigmatism.10,11 Koch et al.11 found that vertical alignment decreased in the group of patients in their 20s from 78% to 32% in the group of patients in their 70s. Although there is a stronger decrease than in our study (77% to 48%, respectively), the tendencies are similar to ours. Furthermore Koch et al.11 described that posterior horizontal alignment increased from 0% to 7%, Ho et al.9 from 0 to 9.1% (using polar values), respectively. Again these findings differ only marginally from ours (3% to 8%, respectively). Finally, Koch et al.11 showed similar correlations between the magnitude of anterior and posterior astigmatism depending on the alignment of anterior astigmatism, even though our correlations are stronger. The correlations are r = 0.56 with vertical, r = 0.37 with oblique, and r = −0.08 with horizontal alignment of anterior astigmatism (our correlations are r = 0.77, r = 0.50, and r = 0.41, respectively). Koch et al.11 used a Galilei dual Scheimpflug analyzer (Ziemer Group) for their study, which combines the data taken by a dual-channel Scheimpflug camera with the data from a Placido disk system. Despite the different algorithms and measuring techniques of the Pentacam and the Galilei dual Scheimpflug analyzer, the similarity of the results is remarkable. 
Table 4.
 
Published Values of Mean Posterior Astigmatism
Table 4.
 
Published Values of Mean Posterior Astigmatism
Study* Imaging Modality Used Eyes/Patients, n Mean Age, y ± SD Posterior Astigmatism, D
Mean ± SD Range
Royston1 Purkinje images (Polaroid camera) 5/5 0.38† 0.17–0.78
Dunne3 Purkinje images (Polaroid camera) 60/60 22.3 ± 3.3 0.26†
Prisant7 Scanning-slit topography (Bausch & Lomb Orbscan) 40/31 0.66 ± 0.23 0.32–1.38
Módis8 Scanning-slit topography (Bausch & Lomb Orbscan) 44/44 61.4 ± 16.4 0.78 ± 0.61 0.16–3.30
Dubbelman6 Scheimpflug photography in 6 fixed meridians
 (Topcon SL-45 camera) 114/114 39 ± 14 0.31
Ho10 Rotating Scheimpflug imaging (Oculus Pentacam)‡ 493/493 41.1 ± 21.9 0.33 0.00–0.94
Koch11 Rotating Scheimpflug imaging (Ziemer Galilei DSA)§ 715/435 55 ± 20 0.30 ± 0.15 0.01–1.10
Current Rotating Scheimpflug imaging (Oculus Pentacam)§ 3818/2233 47.5 ± 15.0 0.33 ± 0.18 0.0–1.35
By default configuration, the TCRP value given by the Pentacam is assessed in the 4-mm zone. This value is used in the clinical setting. For this study, we compared the CASim-K values from the 15° zone with its equivalent, the CATCRP values of the 3-mm zone. Limitations of this study include that both left and right eyes of 1565 patients were analyzed. In addition, all measurements were performed by only one device, the Pentacam HR, thus the accuracy cannot be compared. Values calculated via TCRP are displayed to one decimal point. There are several data points in Figure 2b along the 90° meridian that show remarkably higher CATCRP values than CASim-K. The CApost of these data points is mainly within a small range (up to 0.5 D) and with vertical orientation. If we use CATCRP values measured in the 4-mm zone for these data points instead of CATCRP values from the 3-mm zone used in this study, more than 95% of the regarded data points are located next to the trend line. Thus, these data points (between 1.0% and 1.5% of all data points) are most likely to be errors in measurement. 
In conclusion, mean CApost is −0.33 D and exceeds 0.50 D in 15%. The number of eyes with anterior horizontal alignment increases with increasing age, whereas posterior alignment mostly remains vertical. When anterior alignment is vertical, posterior alignment is most likely vertical and posterior astigmatism partly compensates anterior astigmatism. Thus, CASim-K tends to overestimation. If anterior astigmatism is aligned horizontally, the alignment of posterior astigmatism and therefore the total corneal astigmatism cannot be safely predicted. Ignoring posterior astigmatism can lead to miscalculation of total corneal astigmatism and in cases of toric IOL implantation to significant visual overcorrection or undercorrection. 
Acknowledgments
Presented in part at the annual meeting of the Association for Research in Vision and Ophthalmology, Orlando, Florida, United States, May 2014. 
Disclosure: B. Tonn, None; O.K. Klaproth, RHI-HS (C), Alcon (R), Oculus (R), Rayner (R), Zeiss (R); T. Kohnen, Abbott (C, R), Alcon (C, R), Bausch & Lomb (C, R), Thieme (C, R), Hoya (C, R), Rayner (C, R), Neoptics (C, R), Oculus (C, R), Schwind (C, R), Zeiss (C, R) 
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Figure 1
 
Location of steep meridian on anterior and posterior corneal surfaces.
Figure 1
 
Location of steep meridian on anterior and posterior corneal surfaces.
Figure 2
 
Differences between anterior corneal steep meridian and posterior corneal steep meridian ([a] r = 0.72) and differences in magnitude between CATCRP and CASim-K ([b] r = 0.48) as a function of the anterior corneal steep meridian.
Figure 2
 
Differences between anterior corneal steep meridian and posterior corneal steep meridian ([a] r = 0.72) and differences in magnitude between CATCRP and CASim-K ([b] r = 0.48) as a function of the anterior corneal steep meridian.
Figure 3
 
Differences between anterior corneal steep meridian and posterior corneal steep meridian as a function of the differences in magnitude between CATCRP and CASim-K (r = 0.62). Eyes with anterior steep meridian aligned horizontally and posterior steep meridian aligned vertically are in black, other combinations of alignment are in gray.
Figure 3
 
Differences between anterior corneal steep meridian and posterior corneal steep meridian as a function of the differences in magnitude between CATCRP and CASim-K (r = 0.62). Eyes with anterior steep meridian aligned horizontally and posterior steep meridian aligned vertically are in black, other combinations of alignment are in gray.
Figure 4
 
Percentage of eyes with vertical, horizontal, and oblique steep meridian in each decade on anterior corneal surface (a) and posterior corneal surface (b).
Figure 4
 
Percentage of eyes with vertical, horizontal, and oblique steep meridian in each decade on anterior corneal surface (a) and posterior corneal surface (b).
Figure 5
 
Magnitude of astigmatism on the anterior corneal surface and posterior corneal surface grouped according to the orientation of the steep meridian on the anterior cornea. (a) vertical (r = 0.77); (b) oblique (r = 0.50); (c) horizontal (r = 0.41).
Figure 5
 
Magnitude of astigmatism on the anterior corneal surface and posterior corneal surface grouped according to the orientation of the steep meridian on the anterior cornea. (a) vertical (r = 0.77); (b) oblique (r = 0.50); (c) horizontal (r = 0.41).
Figure 6
 
Differences between CATCRP and CASim-K as a function of CASim-K. Differences that exceed 50% of CASim-K are in black.
Figure 6
 
Differences between CATCRP and CASim-K as a function of CASim-K. Differences that exceed 50% of CASim-K are in black.
Table 1.
 
Aggregate Anterior and Posterior Corneal Astigmatism
Table 1.
 
Aggregate Anterior and Posterior Corneal Astigmatism
Age, y Eyes Mean ± SD, D
Anterior Cornea Posterior Cornea
20–29 561 1.13 ± 1.15 at 88.79° −0.33 ± 0.19 at 87.71°
30–39 680 0.85 ± 1.04 at 88.73° −0.28 ± 0.18 at 87.79°
40–49 895 0.94 ± 1.04 at 88.21° −0.29 ± 0.18 at 88.21°
50–59 775 0.89 ± 0.94 at 88.32° −0.30 ± 0.17 at 88.49°
60–69 536 0.54 ± 0.81 at 88.99° −0.23 ± 0.16 at 89.36°
70–79 362 0.21 ± 0.82 at 87.64° −0.21 ± 0.17 at 88.13°
Table 2
 
Corneal Astigmatism Magnitude, n = 3818
Table 2
 
Corneal Astigmatism Magnitude, n = 3818
Parameter Magnitude, D Percentage of Eyes
Mean ± SD Range ≤0.25 D ≤0.50 D ≤0.75 D ≤1.00 D
CATCRP 1.13 ± 0.89 0–7.2 26.4 60.0
CASim-K 1.15 ± 0.90 0–7.27 6.4 22.5 38.6 55.1
CAant 1.28 ± 1.01 0–8.10 5.3 19.0 33.2 49.0
CApost −0.33 ± 0.18 0 to −1.35 35.2 85.0 97.4 99.6
Table 3
 
Over- and Underestimation of Total Corneal Astigmatism
Table 3
 
Over- and Underestimation of Total Corneal Astigmatism
Age, y Eyes Magnitude CATCRP – CASim-K, D
Mean ± SD Range
20–29 561 −0.10 ± 0.23 −0.94 to 1.53
30–39 680 −0.05 ± 0.25 −0.84 to 2.37
40–49 895 −0.06 ± 0.25 −0.84 to 1.82
50–59 775 −0.03 ± 0.27 −0.87 to 2.42
60–69 536 0.05 ± 0.31 −0.88 to 1.67
70–79 362 0.10 ± 0.31 −1.11 to 2.58
Table 4.
 
Published Values of Mean Posterior Astigmatism
Table 4.
 
Published Values of Mean Posterior Astigmatism
Study* Imaging Modality Used Eyes/Patients, n Mean Age, y ± SD Posterior Astigmatism, D
Mean ± SD Range
Royston1 Purkinje images (Polaroid camera) 5/5 0.38† 0.17–0.78
Dunne3 Purkinje images (Polaroid camera) 60/60 22.3 ± 3.3 0.26†
Prisant7 Scanning-slit topography (Bausch & Lomb Orbscan) 40/31 0.66 ± 0.23 0.32–1.38
Módis8 Scanning-slit topography (Bausch & Lomb Orbscan) 44/44 61.4 ± 16.4 0.78 ± 0.61 0.16–3.30
Dubbelman6 Scheimpflug photography in 6 fixed meridians
 (Topcon SL-45 camera) 114/114 39 ± 14 0.31
Ho10 Rotating Scheimpflug imaging (Oculus Pentacam)‡ 493/493 41.1 ± 21.9 0.33 0.00–0.94
Koch11 Rotating Scheimpflug imaging (Ziemer Galilei DSA)§ 715/435 55 ± 20 0.30 ± 0.15 0.01–1.10
Current Rotating Scheimpflug imaging (Oculus Pentacam)§ 3818/2233 47.5 ± 15.0 0.33 ± 0.18 0.0–1.35
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