

ORIGINAL ARTICLE 

Year : 2015  Volume
: 108
 Issue : 2  Page : 7478 

Studying the contribution of posterior corneal astigmatism to total corneal astigmatism
Hany Ahmed Helaly
Department of Ophthalmology, Faculty of Medicine, Alexandria University, Alexandria, Egypt
Date of Submission  22Jan2015 
Date of Acceptance  24Apr2015 
Date of Web Publication  23Jul2015 
Correspondence Address: Hany Ahmed Helaly 30 Roshdy Street, Roshdy, Alexandria 21529 Egypt
Source of Support: None, Conflict of Interest: None  Check 
DOI: 10.4103/20900686.161397
Settings The Faculty of Medicine, Alexandria University, Egypt. Purpose The aim of this work was to study the contribution of posterior corneal astigmatism to total corneal astigmatism. Patients and methods A descriptive prospective observational study that included 100 eyes of 100 patients aged 18 years and above. Scheimpflug camera imaging was performed using a Pentacam. The following data were recorded: anterior corneal radii of curvature, posterior corneal radii of curvature and astigmatism, simulated keratometry (sim K) and astigmatism, the true net power and astigmatism, and central corneal pachymetry. All included participants signed a written informed consent. Results The mean age was 38.11 ± 12.69 years. The orientation of the steep axis of the anterior corneal surface was vertical in 70% of the cases, resulting in withtherule astigmatism. For the posterior corneal surface, the steep axis orientation was vertical in 94% of the cases, resulting in againsttherule (ATR) astigmatism. The mean sim K astigmatism was higher than that of the true net K astigmatism by 0.12 ± 0.18 D (range 0.30.4 D) at 4 ± 5° (range 021°). Conclusion Anterior corneal withtherule astigmatism tends to change to ATR astigmatism with age. The posterior corneal surface showed ATR astigmatism regardless of the age. Using data from the anterior corneal surface only resulted in a higher astigmatism of 0.12 D compared with using data from both the anterior and the posterior surfaces. Also, data from the anterior corneal surface alone resulted in a difference in the axis of more than 10° in 11% of the cases. Keywords: Corneal astigmatism, corneal power, posterior cornea
How to cite this article: Helaly HA. Studying the contribution of posterior corneal astigmatism to total corneal astigmatism. J Egypt Ophthalmol Soc 2015;108:748 
How to cite this URL: Helaly HA. Studying the contribution of posterior corneal astigmatism to total corneal astigmatism. J Egypt Ophthalmol Soc [serial online] 2015 [cited 2023 Feb 1];108:748. Available from: http://www.jeos.eg.net/text.asp?2015/108/2/74/161397 
Introduction   
Modern cataract surgery with the implantation of premium intraocular lenses (IOLs) necessitates minimum postoperative astigmatism. Residual refractive postoperative astigmatism is of special importance in patients with multifocal IOLs [1],[2],[3],[4]. As little as 0.5 D of postoperative residual astigmatism can have an irritating effect on the visual outcome of the patient [5]. Accurate calculation of corneal astigmatism is also important in choosing the toric IOL to be implanted during cataract surgery. Depending only on the anterior surface of the cornea can lead to undercorrection or overcorrection of the astigmatism [6],[7],[8],[9],[10].
There are different instruments used to calculate corneal astigmatism. The manual keratometer designed by Javal and Schiψtz depended on measuring the radius of curvature of the anterior surface of the cornea and used a keratometric index to represent the total corneal astigmatism (TCA) [11],[12],[13],[14]. This was followed by autokeratometers and topographers that also depended on the anterior surface curvature and keratometric index transformation [14],[15],[16],[17].
Newer machines using Scheimpflug imaging and optical coherence tomography can measure the posterior corneal astigmatism (PCA) [5],[18],[19]. Calculation of the TCA taking into consideration both the anterior and the posterior corneal surfaces can be performed using vector analysis [19],[20]. Ray tracing calculates the TCA directly and has the advantage of avoiding paraxial assumptions [21],[22].
This study aimed at studying the contribution of the PCA to the TCA.
Patients and methods   
This descriptive prospective observational study was approved by the local research ethics committee in the Faculty of Medicine, Alexandria University, Egypt. The tenets of Declaration of Helsinki were followed. All included participants were informed about the use of their personal information and signed a written informed consent. One hundred eyes (right eye) of 100 patients attending the outpatient ophthalmology clinic were included. Patients included had clear healthy cornea with no previous ocular surgery or morbidity, and were not contact lens wearers. Patients to be included were aged 18 years and above.
Scheimpflug camera imaging was performed using a Pentacam (Oculus, Wetzlar, Germany). An average of three goodquality scans that were checked OK by the machine was used to obtain the data. The following data were recorded: anterior corneal radii of curvature, posterior corneal radii of curvature and astigmatism, simulated keratometry (sim K) astigmatism, the true net power and astigmatism, and central corneal pachymetry. Gaussian optics formulas that use paraxial approximation were used to calculate anterior, posterior, and TCA. The power and the curvature are proportional in the central paraxial region [6],[23].
(1) The radii of curvature of the anterior corneal surface were used to calculate anterior corneal astigmatism (ACA) as follows:
Power (D) = (n_{c}  n_{0} )/r_{ant,}
where n_{c} is the index of refraction of the cornea, which equals 1.376; n_{0} is the index of refraction of the air, which equals 1.0; and r_{ant} is the radius of curvature in meters.
(2) The radii of curvature of the posterior corneal surface were used to calculate PCA as follows:
Power (D) = (n_{aq}  n_{c} )/r_{post,}
where n_{aq} is the index of refraction of the aqueous, which equals 1.336 and r_{post} is the radius of curvature in meters.
(3) The true net power and astigmatism are calculated by the Pentacam software. It uses the real anterior curvature, the posterior curvature, and the corneal thickness values with a modified refractive index rather than the real refractive index of air, cornea, and aqueous [24]. Theoretically, the total corneal power and TCA are calculated using the Gaussian optics formula for thick lenses, which uses paraxial approximation as follows:
F_{total} = F_{1} +F_{2} (d/n_{c} )(F_{1}ΧF_{2} ),
where F_{total} is the total corneal power calculated in diopters; F_{1} is the power of the anterior corneal surface in diopters; F_{1} is the power of the anterior corneal surface in diopters; F_{2} is the power of the posterior corneal surface in diopters; and d is the central corneal pachymetry in meters.
(4) Sim K astigmatism use the radii of curvature of the anterior corneal surface only with a lower refractive index (n = 1.3375) to account for the posterior surface divergent effect without actually measuring it. It is calculated by the averaging power obtained from the anterior corneal radius measured along the 3.0mm central ring [25].
For the anterior corneal surface, a vertical steep meridian results in withtherule (WTR) astigmatism. The reverse is true for the posterior corneal surface, where a vertical steep meridian results in againsttherule (ATR) astigmatism. The vertical meridian is considered as a meridian with axis 90 ± 30° (range 60120°). The horizontal meridian is considered as a meridian with axis 180 ± 30° (range 030° and 150180°). The oblique meridian is considered as a meridian with an axis in between.
Clinical findings were statistically evaluated using Excel 2007 (Microsoft Corp.) and SPSS software (version 15.0; SPSS Inc., Chicago, Illinois, USA). Means and SD were calculated. To check for normal distribution, the KolmogorovSmirnov test was applied. Comparisons of the means of normally distributed data were performed with the ttest. Percentages of the steep meridian orientation for the ACA and the PCA were calculated. The χ^{2} test was used to compare different percentages. A P value less than 0.05 was considered statistically significant. The Pearson correlation coefficient (r) was used to correlate between variables.
Results   
The study included 100 right eyes of 54 female and 46 male participants. The mean age was 38.11 ± 12.69 years (range 2064 years). [Table 1] and [Figure 1] show the descriptive data of ACA, PCA, TCA, and sim K astigmatism. The mean cylinder for ACA was 1.77 ± 1.22 D, for PCA was 0.42 ± 0.20 D, for TCA 1.46 ± 1.0 D, and for sim K astigmatism was 1.58 ± 1.11 D.
The mean corneal power of the anterior corneal surface was 48.45 ± 1.96 D (range 44.852.1 D), that of the posterior corneal surface was 6.30 ± 0.27 D (range 5.7 to 6.8 D), the total corneal power was 42.26 ± 1.76 D (range 38.345.7 D), and sim K astigmatism was 43.62 ± 1.76 D (range 40.447.0 D).
The orientation of the steep axis of the anterior corneal surface was vertical in 70% of the cases resulting in WTR astigmatism. For the posterior corneal surface, the steep axis orientation was vertical in 94% of the cases resulting in ATR astigmatism. A subgroup analysis showed that 88% of the participants who were less than 40 years old had vertical steep axis of the anterior corneal surface against 60% of the participants who were more than 40 years old (P < 0.001). The vertical orientation of the steep axis of the posterior corneal surface was present in 96% of the participants who were less than 40 years old against 92% of the participants who were more than 40 years old (P = 0.234).
Correlation between the magnitude of the anterior and the PCA among the included participants showed good correlation (R^{2} = 0.731, P < 0.001). A subgroup analysis showed a strong correlation in participants less than 40 years old (R^{2} = 0.861, P < 0.001) and a weak correlation in participants more than 40 years old (R^{2} = 0.307, P = 0.077). Also, subgroup analysis showed good correlation in cases of anterior corneal WTR astigmatism (R^{2} = 0.750, P < 0.001) and good correlation in cases of anterior corneal ATR astigmatism (R^{2} = 0.746, P < 0.001).
The mean ratio between the magnitudes of the PCA and the ACA was 0.286 ± 0.124. A subgroup analysis showed a mean ratio of 0.265 ± 0.113 in participants less than 40 years old and 0.334 ± 0.140 in participants more than 40 years old (P = 0.123). In cases of anterior corneal WTR astigmatism, the mean ratio was 0.277 ± 0.126, and in cases of anterior corneal ATR astigmatism the mean ratio was 0.270 ± 0.135 (P = 0.782).
The mean ratio between the radii of curvature of the anterior corneal surface and the posterior corneal surface was 0.819 ± 0.021. In participants less than 40 years old, the mean ratio was 0.821 ± 0.015 against 0.814 ± 0.031 in participants more than 40 years old. In cases of anterior corneal WTR astigmatism, the mean ratio was 0.818 ± 0.023 and in cases of anterior corneal ATR astigmatism the mean ratio was 0.822 ± 0.015.
The mean vector for the TCA true net K was 1.46 ± 1.0 D at 100 ± 42°. The mean vector for sim K astigmatism was 1.58 ± 1.11 D at 99 ± 39°. The vector difference [Table 2] showed that mean sim K astigmatism was higher than that of true net K astigmatism by 0.12 ± 0.18 D (range −0.30.4 D) at 4 ± 5° (range 021°). The mean absolute difference was 0.19 ± 0.11 D (range 0.00.4 D).
Using the ttest to compare the mean difference in the magnitude between sim K astigmatism and true net K astigmatism, the difference was statistically significant (t = 4.117, P < 0.001). They showed high correlation (r = 0.991, P < 0.001). Using the ttest to compare the mean difference in the axis between sim K astigmatism and true net K astigmatism, the difference was not statistically significant (t = −1.590, P = 0.121). They showed high correlation (r = 0.992, P < 0.001).  Table 2: Difference between stimulated K astigmatism and true net K astigmatism
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The difference in the magnitude between sim K astigmatism and true net K astigmatism was less than 0.5 D in all cases. The difference in the axis between sim K astigmatism and true net K astigmatism was 10° or less in 89% of the patients and more than 10° in 11% of the patients (all of them had sim K astigmatism and true net K astigmatism of <1 D).
Discussion   
Modern machines such as Scheimpflug imaging allowed direct measurement of the posterior corneal surface. This is an advantage over older machines that measured only the anterior corneal surface and used the refractive index to account for the posterior corneal surface contribution. Srivannaboon et al. [30] showed a comparable mean axis and magnitude in astigmatism between sim K astigmatism and autorefractometer keratometry.
The steep axis alignment of the anterior corneal surface was vertical (60120°) in 70% of the included eyes, resulting in WTR astigmatism. Koch et al. [5] studied the contribution of PCA with TCA using a dualScheimpflug analyzer. They analyzed 715 corneas of 435 consecutive patients. Their results showed that the steep corneal meridian was aligned vertically in 51.9% of the eyes for the anterior corneal surface. The difference in the percentage from the current study may be contributed to a difference in the mean age of the included participants.
The subgroup analysis showed a significant change of the orientation of the vertical steep axis of the anterior corneal surface towards the oblique or the horizontal axis with increasing age (88% of the participants <40 years old vs. 60% of the participants >40 years old). Ho et al. [26] evaluated agerelated changes in the astigmatism of the anterior corneal surface and concluded that the proportion of WTR astigmatism decreased and those of oblique and ATR astigmatisms increased with age.
The steep axis alignment of the posterior corneal surface was vertical (60120°) in 94% of the included eyes, resulting in ATR astigmatism. This vertical orientation agreed with previously published results of other studies [5],[19]. A subgroup analysis did not show a significant change in the vertical orientation of the steep axis of the posterior corneal surface with age (96% of the participants <40 years old vs. 92% of the participants >40 years old).
Ratσn et al. [6] studied the composition of corneal astigmatism in older adults. They included 100 consecutive patients aged between 60 and 80 years. They showed that PCA was 87% against the rule.
The mean cylinder for the posterior corneal surface was 0.42 ± 0.20 D. This was slightly higher than the results published by Koch et al. [5] and Ho et al. [19] (0.30 D using a Galilei topographer and 0.29 D using Pentacam, respectively). Ratσn et al. [6] published a mean PCA of 0.38 D in their study that included old aged patients.
The mean ratio of the radii of curvature of the anterior corneal surface to the posterior corneal surface was almost the same (0.82) regardless of the age or the steep axis orientation. The magnitude of the anterior and the PCA showed good correlation, except in the older age group above 40 years, which showed a weaker correlation. Results published by Montalbαn et al. [27],[28],[29] stated that the toricity and the astigmatic power vector components of the posterior corneal surface in the human healthy eye are related to those of the anterior corneal surface. Although Koch et al. [5] and Ho et al. [26] concluded that the magnitude of the anterior corneal ATR astigmatism seemed to be poorly correlated with the PCA magnitude, they also concluded that the magnitude of the anterior corneal WTR and oblique astigmatism had a direct correlation with the PCA magnitude.
Calculating the corneal astigmatism from only anterior corneal surface data (sim K astigmatism) resulted in a higher astigmatism than using data from both anterior and posterior corneal surfaces (true net power). The mean arithmetic error was 0.12 ± 0.18 D and the mean absolute error was 0.19 ± 0.11 D. The difference in all cases was less than 0.5 D (range 0.30.4 D). A toric IOL is presented in a 0.5 D scale, so that a difference of less than 0.5 D will not affect the choice of the implanted toric IOL. The difference in axis between sim K astigmatism and true net K astigmatism was more than 10° in 11% of the patients, which would lead to a change in the choice of the implanted toric IOL. However, all of these cases had a sim K astigmatism and a true net K astigmatism of less than 1 D.
In conclusion, anterior corneal WTR astigmatism tends to change to ATR astigmatism with age. The posterior corneal surface showed ATR astigmatism regardless of the age. Using data from the anterior corneal surface only resulted in a higher astigmatism of 0.12 D than using data from both anterior and posterior surfaces. Also, data from the anterior corneal surface alone resulted in a difference in axis of more than 10° in 11% of the cases. TCA calculated from both anterior and posterior surface data could be used in the toric IOL calculator instead of that calculated from the anterior corneal surface alone.
Acknowledgements   
Conflicts of interest
There are no conflicts of interest.
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[Figure 1]
[Table 1], [Table 2]
