Journal of Refractive Surgery

Original Article Supplemental Data

Agreement Between Internal Astigmatism and Posterior Corneal Astigmatism in Pseudophakic Eyes

Sepehr Feizi, MD, MSc; Siamak Delfazayebaher, MD; Mohammad Ali Javadi, MD

Abstract

PURPOSE:

To directly measure internal astigmatism and evaluate its agreement with posterior corneal astigmatism in pseudophakic eyes.

METHODS:

This prospective study enrolled 32 eyes of 32 patients (18 women, 56.3%) who underwent phacoemulsification with implantation of a non-toric monofocal intraocular lens (IOL). Two months postoperatively, posterior corneal astigmatism was measured using a Pentacam Scheimpflug analyzer (Oculus Optikgeräte GmbH, Wetzlar, Germany). Manifest refractive astigmatism was measured after fitting a spherical hard contact lens. This refractive astigmatism that was vertexed to the corneal plane was considered internal astigmatism. The magnitudes of internal and posterior corneal astigmatism were compared. The relationship and agreement between these two astigmatisms were investigated using the Spearman correlation coefficient and Bland–Altman plots, respectively.

RESULTS:

The mean patient age was 56.3 ± 9.6 years. IOL decentration or tilt and posterior segment abnormalities were not encountered in any cases postoperatively. The mean refractive astigmatism measured before fitting the hard contact lens was −0.81 ± 0.56 diopters (D). Internal astigmatism (−0.17 ± 0.21 D) was significantly different from posterior corneal astigmatism (−0.30 ± 0.15 D; P = .046). Regression analysis demonstrated a weak association between internal astigmatism and posterior corneal astigmatism (r2 = 0.22, P = .013). Bland–Altman plots produced 95% limits of agreement for these two astigmatisms from −0.49 to 0.75 D.

CONCLUSIONS:

A significant but weak correlation was found between the magnitudes of internal astigmatism and posterior corneal astigmatism in the pseudophakic eyes. This result indicates that Pentacam measurement of the posterior cornea did not compare well with a “gold standard” of refraction-derived values.

[J Refract Surg. 2018;34(6):379–386.]

Abstract

PURPOSE:

To directly measure internal astigmatism and evaluate its agreement with posterior corneal astigmatism in pseudophakic eyes.

METHODS:

This prospective study enrolled 32 eyes of 32 patients (18 women, 56.3%) who underwent phacoemulsification with implantation of a non-toric monofocal intraocular lens (IOL). Two months postoperatively, posterior corneal astigmatism was measured using a Pentacam Scheimpflug analyzer (Oculus Optikgeräte GmbH, Wetzlar, Germany). Manifest refractive astigmatism was measured after fitting a spherical hard contact lens. This refractive astigmatism that was vertexed to the corneal plane was considered internal astigmatism. The magnitudes of internal and posterior corneal astigmatism were compared. The relationship and agreement between these two astigmatisms were investigated using the Spearman correlation coefficient and Bland–Altman plots, respectively.

RESULTS:

The mean patient age was 56.3 ± 9.6 years. IOL decentration or tilt and posterior segment abnormalities were not encountered in any cases postoperatively. The mean refractive astigmatism measured before fitting the hard contact lens was −0.81 ± 0.56 diopters (D). Internal astigmatism (−0.17 ± 0.21 D) was significantly different from posterior corneal astigmatism (−0.30 ± 0.15 D; P = .046). Regression analysis demonstrated a weak association between internal astigmatism and posterior corneal astigmatism (r2 = 0.22, P = .013). Bland–Altman plots produced 95% limits of agreement for these two astigmatisms from −0.49 to 0.75 D.

CONCLUSIONS:

A significant but weak correlation was found between the magnitudes of internal astigmatism and posterior corneal astigmatism in the pseudophakic eyes. This result indicates that Pentacam measurement of the posterior cornea did not compare well with a “gold standard” of refraction-derived values.

[J Refract Surg. 2018;34(6):379–386.]

Internal astigmatism, which is the discrepancy between refractive and keratometric astigmatism, is the element of total ocular astigmatism that is not caused by the anterior corneal surface. The magnitude of internal astigmatism varies between 0.07 and 2.58 diopters (D), with a mean value of 0.79 D, in normal eyes.1 This astigmatism provides a compensatory effect for anterior corneal astigmatism, which is predominantly with-the-rule.2 The contribution of internal astigmatism to refractive astigmatism has been of interest to surgeons desiring to determine the optimal power for the toric intraocular lens (IOL) and to predict outcomes of corneal refractive surgery.3–5

Lenticular astigmatism has been considered the most common cause of internal astigmatism.6 The remaining factors considered responsible for this type of astigmatism include posterior corneal surface, misalignment of internal ocular surfaces, an irregular index of refraction, and some unknown retinal and cortical components.3,7–9 Previous studies reported that incorporating posterior corneal astigmatism into the toric IOL calculation improves refractive outcomes.10–15 The development of new technologies, including optical coherence tomography (OCT) and Scheimpflug devices, has made the quantitative evaluation of the posterior corneal surface in a clinical setting possible.7,8,16 However, the precision of posterior corneal surface measurements has not been fully confirmed, and some investigators suggest that the repeatability of Scheimpflug devices can be lower for this surface than for the anterior corneal surface.10,17,18

Because some of the studies have reached contradictory conclusions regarding the accuracy of posterior corneal Scheimpflug imaging, the current study investigated the precision of posterior corneal astigmatism as measured by a rotating Scheimpflug camera. Unfortunately, there is no benchmark for the measurement of posterior corneal astigmatism, and the only way to validate the precision of the measurements by this technology is by refracting the eyes and eliminating other causes of astigmatism, including anterior corneal and lenticular astigmatism. In the current study, we directly measured internal astigmatism in pseudophakic eyes implanted with spherical IOLs to eliminate lenticular astigmatism. This astigmatism was compared with the posterior corneal astigmatism measured by the Pentacam (Oculus Optikgeräte GmbH, Wetzlar, Germany).

Patients and Methods

This study was a prospective non-randomized interventional case series conducted on patients with cataract who were referred for phacoemulsification between January and June 2016. Because patients with a high amount of corneal astigmatism routinely receive a toric IOL during cataract surgery, the study included participants with low to moderate corneal astigmatism who were scheduled to have spherical IOL implants. Only one eye from each patient with postoperative corrected distance visual acuity (CDVA) of 20/25 or better was enrolled to make refraction assessment accurate. A signed informed consent was obtained from all participants after explaining the purposes of the study, which was conducted according to the tenets of the Declaration of Helsinki, including acceptance by the Institutional Review Board of the Ophthalmic Research Center. The exclusion criteria were history of previous corneal or intraocular surgery; history of ocular disease, including dry eye, keratoconus, glaucoma, abnormal iris, pupil deformation, ocular inflammation, or posterior segment pathologies (eg, retinal detachment and macular degeneration); and any intraoperative complication, such as wound burn, zonular dehiscence, continuous curvilinear capsulorhexis rim tear, posterior capsular rupture or vitreous loss, failure to place the IOL in the capsular bag, postoperative IOL decentration or tilt, posterior capsular opacification, and macular edema.

Preoperative Examination

A complete examination, including uncorrected distance visual acuity (UDVA) and CDVA, manifest refraction, applanation tonometry, slit-lamp biomicroscopy, and dilated fundus examination, was performed. Biometric measurements were performed with a Zeiss IOLMaster 500 (version 5.4.4.0006; Carl Zeiss Meditec AG, Oberkochen, Germany). Based on the axial length, the Hoffer Q, Holladay 1, or SRK/T formula was used for IOL power calculation.19

Postoperative Examinations and Measurements

All patients were reexamined on postoperative days 1, 3, 7, 30, and 60. At the 2-month postoperative visit, a thorough clinical ophthalmological examination was performed, including manifest refraction, UDVA and CDVA with a decimal visual acuity chart, and slit-lamp biomicroscopy. Manifest refraction was objectively measured using an autokeratorefractometer (software version 1.2.6; Carl Zeiss Meditec AG), followed by subjective refraction by a single expert optometrist. Subjective refraction was performed at a vertex distance of 12 mm using a trial frame with an accuracy of ±0.25 D in sphere and cylinder magnitude and 5° accuracy in astigmatic orientation. The axis and power of refractive astigmatism were refined using a Jackson cross-cylinder ±0.25 D. First, the astigmatism axis was refined by swiftly turning the cross-cylinder using the “handle on axis” approach. Afterward, the acquired astigmatism magnitude was fine-tuned by swiftly turning the cross-cylinder “axis on axis” and adjusting the refractive astigmatism accordingly.

Next, the Pentacam Scheimpflug analyzer (Pentacam HR, software version 1.17r139) was used to measure simulated keratometric astigmatism and posterior corneal astigmatism. The device was calibrated before each measurement. Briefly, the patient stared at the fixation target on the black background in the center of the blue fixation beam. The instrument automatically measured 25,000 data points over the cornea within 2 seconds using an apex-centered approach. The power and axis of keratometric and posterior corneal astigmatism were determined within the central 3 mm. Default refractive indexes for the cornea (1.376) and aqueous humor (1.336) were used to calculate posterior corneal astigmatism. The measurements were confirmed under a quality-specification window. Good-quality, well-centered images (Quality Specification OK) were included in the study. If the image quality was not acceptable, then the examination was repeated or the patient's data were excluded. The average values of three high-quality Pentacam measurements were recorded for each eye.

Manifest refraction was measured after fitting a spherical rigid gas-permeable contact lens. The rigid gas-permeable lenses were fitted by the same optometrist with a trial fitting set (BIAS, Hecht, Germany). The lens diameter was 9.6 mm, and the range of base curve radius values was 7.2 to 8.3 mm. The initial base curve radius was selected to be 0.1 mm smaller than that indicated by simulated flat keratometry readings. The base curve radius was then decreased or increased in 0.1-mm increments to achieve a well-centered fit. The centration of the rigid gas-permeable contact lens was carefully examined using the slit lamp. After an appropriate rigid gas-permeable lens was fitted, manifest refractive astigmatism was measured objectively using the autokeratorefractometer and then refined subjectively in the same way as described earlier. This astigmatism, which included posterior corneal astigmatism and perhaps astigmatism caused by IOL, was defined as internal astigmatism. Because the measurements were made in pseudophakic eyes, the astigmatism induced by the crystalline lens was naturally eliminated. To facilitate comparison between internal astigmatism and posterior corneal astigmatism, the power of internal astigmatism was transformed from vertex (12 mm) to corneal plane according to Holladay et al.20 Both internal astigmatism and posterior corneal astigmatism were expressed using negative cylinder notation.

The last examination was the evaluation of IOL position, capsular bag, and posterior pole using the slit lamp. After pupil dilation with tropicamide 1.0% and phenylephrine hydrochloride 2.5%, the IOL was carefully examined for the presence of IOL tilting and decentration and posterior capsule was examined for shrinkage and opacification. The retina was evaluated for any abnormalities, including posterior staphyloma.

UDVA and CDVA were transformed into logMAR units before statistical analysis. The magnitudes of internal astigmatism and posterior corneal astigmatism were compared using power vector analysis according to Thibos and Horner.21 Each astigmatism value was transformed to rectangular vectors J0 and J45 using the following formulas: J0 = −(C/2) × Cos (2α) and J45 = − (C/2) × Sin (2α), where J0 is the Jackson cross-cylinder power at axis 90° and 180°, J45 is the Jackson cross-cylinder power at axis 45° and 135°, C is the negative cylinder, and is the axis of the flat meridian. In addition, the vector analysis of each astigmatism was performed using the Alpins vectorial method (Assort software; Assort Pty, Ltd., Victoria, Australia).22

Statistical Analysis

A sample size calculation was performed to detect a difference of 0.15 D between internal astigmatism and posterior corneal astigmatism. The data of the initial 10 eyes exhibited that the standard deviation of the difference was 0.20 D. For a test power of 85% and a significance level of 5%, 32 eyes were required. Data were analyzed using SPSS statistical software (version 21; IBM Corporation, Armonk, NY). A Kolmogorov–Smirnov test and Q-Q plot were used to evaluate the normality of continuous variables. The magnitudes of two astigmatisms and their vector components (J0 and J45) were compared using the Wilcoxon signed-rank test. The Spearman correlation coefficient and linear regression analysis were used to investigate relationships between internal astigmatism and posterior corneal astigmatism in terms of the magnitudes, J0, and J45. Bland–Altman plots and the 95% limits of agreement (mean difference ± 1.96 standard deviation) were applied to determine the agreement between these two astigmatisms with respect to magnitude, axis orientation, and vector components. A P value of less than .05 was considered statistically significant. All P values were two-sided.

Results

Thirty-six eyes of 36 patients were initially enrolled. Postoperative CDVA was less than 20/25 in 4 eyes, presumably due to anisometropic amblyopia. These eyes were excluded. Therefore, data of 32 eyes (17 right eyes) of 32 patients (18 women) were enrolled for analysis. Cataracts were age related in 28 eyes and developed as a result of prolonged systemic use of corticosteroids in 4 eyes. The mean age at the time of the surgery was 56.3 ± 9.6 years (range: 35 to 73 years).

Table A (available in the online version of this article) summarizes preoperative biometric measurements and implanted IOL power. The mean postoperative UDVA and CDVA were 0.14 ± 0.12 logMAR (range: 0.0 to 0.40 logMAR) and 0.03 ± 0.05 logMAR (range: 0.0 to 0.10 logMAR), respectively. Postoperative CDVA was 20/20 in 22 eyes (68.8%) and 20/25 in 10 eyes (31.2%). The mean postoperative spherical equivalent refraction and refractive astigmatism were −0.21 ± 0.70 D (range: −1.75 to +1.25 D) and −0.81 ± 0.56 D (range: −2.25 to 0.0 D), respectively. All IOLs were found to be accurately centered at the final follow-up examination.

Preoperative Biometric Data and Implanted Intraocular Lens Power in Eyes That Underwent Phacoemulsification

Table A:

Preoperative Biometric Data and Implanted Intraocular Lens Power in Eyes That Underwent Phacoemulsification

Table B (available in the online version of this article) lists the simulated keratometric and posterior corneal mean power and astigmatism measured by the Pentacam Scheimpflug analyzer. The orientation of the steep meridian of the posterior corneal surface was vertical in 27 eyes (84.4%) and oblique in 5 eyes (15.6%) (Figure A, available in the online version of this article).

Simulated Keratometric and Posterior Corneal Mean Power and Astigmatism in 32 Eyes That Underwent Phacoemulsification and Posterior Chamber Intraocular Lens Implantation

Table B:

Simulated Keratometric and Posterior Corneal Mean Power and Astigmatism in 32 Eyes That Underwent Phacoemulsification and Posterior Chamber Intraocular Lens Implantation

Axis distribution (degrees) of internal astigmatism and posterior corneal astigmatism (diopters) in 32 pseudophakic eyes. D = diopters

Figure A.

Axis distribution (degrees) of internal astigmatism and posterior corneal astigmatism (diopters) in 32 pseudophakic eyes. D = diopters

Internal astigmatism was −0.17 ± 0.21 D (range: −0.56 to 0.00 D). The magnitude of internal astigmatism was zero in 15 eyes (46.9%), between −0.25 and −0.50 D in 12 eyes (37.5%), and greater than −0.50 D in 5 eyes (15.6%) (Figure A). There was a significant difference between internal astigmatism and posterior corneal astigmatism (P = .046), although the magnitude of the difference (mean 0.13 D) was small. The magnitude of internal astigmatism was within ±0.50 D of the magnitude of posterior corneal astigmatism in 29 eyes (90.6%).

Table 1 shows the mean J0 and J45 values of internal astigmatism and posterior corneal astigmatism. As demonstrated, there was no significant difference between the internal astigmatic vectors and the posterior corneal astigmatic vectors. The negative values of the J0 astigmatic component indicate against-the-rule astigmatism in internal and posterior corneal astigmatism. The J45 astigmatic component was nearly zero in internal and posterior corneal astigmatism. Figure 1 shows vectors of each astigmatism analyzed using the Alpins method.

Comparisons of Internal Astigmatism and Posterior Corneal Astigmatism in Terms of Jackson Cross-cylinder Component at 0° and 90° (J0) and at 45° and 135° (J45) in 32 Eyes That Underwent Phacoemulsification and Posterior Chamber Intraocular Lens Implantation

Table 1:

Comparisons of Internal Astigmatism and Posterior Corneal Astigmatism in Terms of Jackson Cross-cylinder Component at 0° and 90° (J0) and at 45° and 135° (J45) in 32 Eyes That Underwent Phacoemulsification and Posterior Chamber Intraocular Lens Implantation

Single-angle polar plots for the (A) internal astigmatism and (B) posterior corneal astigmatism. The vector means are plotted as a red cross (calculated in double-angle vector space) and the standard deviations (SDs) for the X and Y axes are displayed in the call-out box. D = diopters

Figure 1.

Single-angle polar plots for the (A) internal astigmatism and (B) posterior corneal astigmatism. The vector means are plotted as a red cross (calculated in double-angle vector space) and the standard deviations (SDs) for the X and Y axes are displayed in the call-out box. D = diopters

Figure 2 shows the Standard Graphs for Reporting Astigmatism. A significant but weak association was found between the magnitudes of internal astigmatism and posterior corneal astigmatism (r2 = 0.22, P = .013). Internal astigmatism could be predicted from posterior corneal astigmatism using the linear regression equation internal astigmatism = −0.36 − (0.65 × posterior corneal astigmatism). There was no statistically significant relationship between internal astigmatism and posterior corneal astigmatism in terms of J0 (r2 = 0.015, P = .54) or J45 (r2 = 0.004, P = .75).

Standard graphs for reporting astigmatism. (A) A histogram of the magnitude of the internal astigmatism (IA) and the magnitude of the posterior corneal astigmatism (PCA). (B) A scattergram illustrating the relationship between IA and PCA. (C) A histogram demonstrating the angle between the axis of the IA and the axis of the PCA. D = diopters

Figure 2.

Standard graphs for reporting astigmatism. (A) A histogram of the magnitude of the internal astigmatism (IA) and the magnitude of the posterior corneal astigmatism (PCA). (B) A scattergram illustrating the relationship between IA and PCA. (C) A histogram demonstrating the angle between the axis of the IA and the axis of the PCA. D = diopters

Bland–Altman plots produced a 95% limits of agreement for the internal astigmatism and posterior corneal astigmatism magnitudes from −0.49 to 0.75 D (mean difference = 0.13 D). This range was −0.27 to 0.30 D (mean difference = 0.01 D) for the J0 values and −0.35 to 0.32 D (mean difference = −0.01 D) for the J45 values (Figure 3).

Bland–Altman plots show the difference between internal astigmatism (IA) and posterior corneal astigmatism (PCA) against the mean of two measurements. (A) Astigmatism magnitude. (B) Axis orientation. (C) Jackson cross-cylinder component at 0° and 90° (J0). (D) Jackson cross-cylinder component at 45° and 135° (J45). The solid lines represent mean differences, and the dotted lines are the upper and lower borders of the 95% limits of agreement. D = diopters

Figure 3.

Bland–Altman plots show the difference between internal astigmatism (IA) and posterior corneal astigmatism (PCA) against the mean of two measurements. (A) Astigmatism magnitude. (B) Axis orientation. (C) Jackson cross-cylinder component at 0° and 90° (J0). (D) Jackson cross-cylinder component at 45° and 135° (J45). The solid lines represent mean differences, and the dotted lines are the upper and lower borders of the 95% limits of agreement. D = diopters

Analysis of the astigmatism axis also showed differences between the internal and posterior corneal astigmatism values. The mean internal astigmatism axis was at 42.2° and the mean posterior corneal astigmatism axis was at 92.8° (P = .001). The percentages of eyes with the internal astigmatism axis within ±5°, ±10°, and ±15° of the posterior corneal astigmatism axis were 7.4%, 11.1%, and 18.5%, respectively (Figure 2). The agreement between the axis of the two astigmatisms was poor: 95% limits of agreement ranged from −164.5° to 63.4° (Figure 3).

Post-hoc power analysis exhibited that our study had a power of 95.9% to detect the observed difference between the magnitudes of internal astigmatism and posterior corneal astigmatism.

Discussion

Previous studies estimated internal astigmatism in pseudophakic eyes implanted with a non-toric IOL through vector subtraction of anterior corneal astigmatism from refractive astigmatism, and they reported a mean vector of internal astigmatism between 0.24 and 0.47 D.23–26 This range is greater than the value we obtained in the current study (0.17 D). Compared to the vector subtraction method, our method can be more accurate because it can prevent errors arising from multistep mathematical calculations and from neglecting the non-alignment of different intraocular surfaces. Our results demonstrate that the posterior corneal astigmatism measured by the Scheimpflug camera weakly correlated with the internal astigmatism. Moreover, vector analysis of astigmatism, which accounts for both astigmatism magnitudes and orientations, showed no significant association between the internal astigmatic vectors and the posterior corneal astigmatic vectors. Thus, the internal astigmatism differed from the posterior corneal astigmatism in both magnitude and axis.

Existing studies of pseudophakic astigmatism only described the association between refractive and keratometric astigmatism.23–26 One study reported a significant but weak association (r = 0.34) between internal astigmatism and posterior corneal astigmatism in normal phakic eyes.1 They attributed this limited correlation to the interaction of several factors (eg, crystalline lens) leading to the internal astigmatism.1 In the current study, where the lenticular component of internal astigmatism was eliminated, the observed weak correlation can be explained by other facts. First, the accuracy of refraction could have introduced bias. Subjective refraction was performed with an accuracy of ±0.25 D in cylinder magnitude, which is greater than the difference found between the internal astigmatism and posterior corneal astigmatism (0.13 D). This could produce noise in the data. If the accuracy had been increased to ±0.12 D, the internal astigmatism would have better matched the posterior corneal astigmatism. Additionally, we calculated the value of internal astigmatism from the astigmatism that was vertexed to the corneal plane. To demonstrate equivalence with posterior corneal astigmatism, it might be necessary to do a second vertex calculation to the posterior corneal surface. Despite these, we believe that the refraction results were still accurate. One experienced optometrist performed autorefraction and subsequent subjective refraction, and only patients with CDVA of 20/25 or better were included, which makes refraction assessment repeatable. Furthermore, we found discrepancies between the directions of internal astigmatism and posterior corneal astigmatism in addition to differences in astigmatism magnitude. Therefore, factors other than bias in refraction can contribute to the difference observed between these two astigmatisms.

Another explanation is the presence of other internal ocular components that could contribute to the internal astigmatism. These components include a tilted or decentered IOL, undetected cylinder in the non-toric IOL, an irregular index of refraction, errors in optical centration, and the retina.3,9 No significant IOL decentration or tilt was detected in any participants of the current study. Using anterior segment OCT for IOL tilt evaluation, Kumar et al.27 demonstrated a mean of 1.52° when the IOLs were placed perfectly in the capsular bag. For an IOL of +22.00 D, this amount of tilt would produce an oblique astigmatism of 0.016 D.28 Therefore, the contribution of the IOL to the internal ocular astigmatism should have been negligible.29 So-called retinal astigmatism may play a role in modifying internal astigmatism. However, a retinoscopic study by Flüeler and Guyton30 dismissed the possible contribution of the retina to ocular refractive astigmatism.

The presence of inaccuracies in posterior corneal curvature measurements by the Pentacam could be the other explanation for our findings. Measurements made by the Scheimpflug device may not reflect the actual refractive power of the posterior cornea. Hoffmann et al.31 considered subjective cylinder to be the standard in pseudophakic eyes and compared objective corneal astigmatism measured by different devices to this standard. They found that, compared to those of other devices, the measurements by the Pentacam rotating Scheimpflug camera had the largest difference vector from the subjective cylinder.31 The authors hypothesized that a single Scheimpflug camera evaluates the measurements too slowly and that the resulting movement artifacts lead to imprecise measurement.31 The results of the current study exhibit that the limits of agreement between the two astigmatism magnitudes were wide (greater than 1.00 D) and crossed the zero line, suggesting poor agreement. This suggests that the Pentacam is not sufficiently accurate and might overestimate posterior corneal astigmatism. We do not have a clear explanation for this finding. A potential explanation can be attributed to the assumption based on which posterior corneal astigmatism is calculated. The Pentacam Scheimpflug analyzer uses a paraxial formula to convert the radius of curvature to diopters with the assumption of parallel rays approaching the posterior corneal surface.32 However, the rays propagating to the posterior corneal surface have already been refracted by the anterior corneal surface. Therefore, the “effective” posterior power will be less than what is calculated using a paraxial formula.33

Regardless of the cause(s) underlying the significant difference between the internal astigmatism and posterior corneal astigmatism, the findings of the current study can have clinical implications. Our results explain why eyes that undergo toric IOL implantation may have astigmatism correction errors postoperatively even if the magnitude of posterior corneal astigmatism is incorporated into the IOL power calculation. The medical literature shows that posterior cornea measurements have on average only a small (although significant) impact on the result of toric IOL calculation because, in most cases, there is residual postoperative astigmatism, which can vary from 0.12 to 0.63 D.10,11,17,34,35

The current study has four limitations. First was lack of access to devices that can measure posterior corneal astigmatism more accurately such as anterior segment OCT. Second, the amount of corneal astigmatism was relatively small in the study group (between 0.10 and 3.10 D). Patients with cataract and considerable corneal astigmatism are routinely candidates for toric IOL implantation and could not be enrolled for the purpose of this study. Third, sample size calculation was performed with a standard deviation of 0.20 D. Given that the precision of the Pentacam is not reported and it may be greater than 0.20 D, and the magnitude of posterior corneal astigmatism was small in the study participants, this standard deviation may be too large to consider it for sample size calculation. However, post-hoc power analysis exhibited that the study has a power of 95.9% to detect the observed difference between the magnitudes of two astigmatisms. Fourth, the number of eyes with each type of anterior corneal astigmatism (with-the-rule, against-the-rule, and oblique) was somewhat small in the current study, precluding the evaluation of agreement between the internal astigmatism and posterior corneal astigmatism in each type of anterior corneal astigmatism.

A weak association was found between the magnitudes of internal astigmatism and posterior corneal astigmatism in pseudophakic eyes. This means Pentacam measurement of the posterior cornea did not compare well with a “gold standard” of refraction-derived values. Additional studies with a larger number of eyes with each type of anterior astigmatism should be performed to increase our knowledge of the accuracy of the currently available methods for determining the cylinder power of toric IOLs.

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Comparisons of Internal Astigmatism and Posterior Corneal Astigmatism in Terms of Jackson Cross-cylinder Component at 0° and 90° (J0) and at 45° and 135° (J45) in 32 Eyes That Underwent Phacoemulsification and Posterior Chamber Intraocular Lens Implantation

ParameterInternal AstigmatismPosterior Corneal AstigmatismP
J0 component (D)−0.018 ± 0.095 (−0.26 to 0.27)−0.032 ± 0.099 (−0.20 to 0.19).68
J45 component (D)−0.004 ± 0.097 (−0.14 to 0.27)0.008 ± 0.136 (−0.29 to 0.35).56

Preoperative Biometric Data and Implanted Intraocular Lens Power in Eyes That Underwent Phacoemulsification

ParameterMean ± Standard DeviationRange
Anterior chamber depth (mm)3.20 ± 0.622.07 to 4.93
Axial length (mm)23.18 ± 1.3520.97 to 26.37
Intraocular lens power (diopters)21.57 ± 3.7118.0 to 25.0

Simulated Keratometric and Posterior Corneal Mean Power and Astigmatism in 32 Eyes That Underwent Phacoemulsification and Posterior Chamber Intraocular Lens Implantation

ParameterSimulated KeratometryPosterior Corneal Surface
Flat power (D)43.78 ± 1.83 (40.10 to 45.20)−6.21 ± 0.30 (−6.80 to −5.70)
Steep power (D)44.80 ± 1.74 (41.50 to 46.60)−6.52 ± 0.32 (−7.20 to −6.0)
Mean power (D)44.27 ± 1.75 (41.50 to 45.90)−6.36 ± 0.29 (−7.0 to −5.90)
Astigmatism power (D)1.02 ± 0.74 (0.10 to 3.10)−0.30 ± 0.15 (−0.70 to −0.10)
Astigmatism axis (degrees)82.3 ± 48.2 (1.6 to 173.2)92.8 ± 19.1 (50.8 to 149.8)
Authors

From the Ophthalmic Research Center and Department of Ophthalmology, Labbafinejad Medical Center, Shahid Beheshti University of Medical Sciences, Tehran, Iran.

The authors have no financial or proprietary interest in the materials presented herein.

AUTHOR CONTRIBUTIONS

Study concept and design (SF, MAJ); data collection (SF, SD); analysis and interpretation of data (SF); writing the manuscript (SF); critical revision of the manuscript (SF, SD, MAJ); statistical expertise (SF)

Correspondence: Sepehr Feizi, MD, MSc, Ophthalmic Research Center, Labbafinejad Medical Center, Boostan 9 Street, Pasdaran Avenue, Tehran 16666, Iran. E-mail address: sepehrfeizi@yahoo.com

Received: December 12, 2017
Accepted: April 20, 2018

10.3928/1081597X-20180425-01

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