## Purpose

To evaluate the accuracy of toric intraocular lens (IOL) calculation using estimated total corneal astigmatism based on the anterior-to-posterior corneal cylinder power ratio according to the axis orientation of anterior corneal astigmatism.

## Design

Retrospective cross-sectional study.

## Methods

Nine hundred twenty-eight eyes of 928 reference subjects and 20 cataract patients (20 eyes) implanted with a toric IOL were enrolled. Linear regression analysis parameters (β _{0 }and β _{1 }) of relationship between the simulated keratometry cylinder (Cyl _{SimK }) and posterior corneal cylinder power of reference subjects were used to calculate the estimated posterior corneal astigmatism (−[β _{1 }× Cyl _{SimK }+ β _{0 }] @ 90). When regression analysis was not significant, estimated posterior corneal astigmatism was defined as the negative value of the mean posterior corneal cylinder power @ 90. Estimated total corneal astigmatism was defined as the vectorial sum of anterior corneal astigmatism and estimated posterior corneal astigmatism. Residual astigmatism error, predicted using SimK, was compared with that predicted using estimated total corneal astigmatism.

## Results

Estimated posterior corneal astigmatism was determined to be −(0.15 × Cyl _{SimK }+ 0.22) @ 90 in eyes with with-the-rule astigmatism, −(0.05 × Cyl _{SimK }+ 0.27) @ 90 in oblique astigmatism, and −0.27 @ 90 in against-the-rule astigmatism. The median magnitude of the predicted residual astigmatism error calculated using estimated total corneal astigmatism (0.30 cylinder diopters) was significantly smaller than that calculated with SimK (0.50 cylinder diopters).

## Conclusions

Toric IOL calculations using estimated total corneal astigmatism based on the anterior-to-posterior corneal cylinder power ratio provided a more appropriate toric IOL cylinder power than calculations using SimK astigmatism.

The cornea is composed of anterior and posterior surfaces. Corneal power and astigmatism can be calculated from the refractive power and astigmatism of each surface using vector analysis. However, devices that measure the posterior corneal surface are not available in all eye clinics. Conventional automated keratometers estimate corneal refractive power and astigmatism from anterior corneal measurements using a fictitious refractive index of corneas.

Toric intraocular lenses (IOLs) have been developed to reduce corneal astigmatism in cataract surgery. The importance of posterior corneal astigmatism and effective toric IOL positions has recently been highlighted. Conventional keratometers, which estimate total corneal astigmatism from anterior corneal measurements, can over- or underestimate corneal astigmatism correction by toric IOLs.

To estimate corneal refractive power from anterior corneal measurements, the fictitious refractive index of the cornea was calculated under the assumption that posterior corneal curvature is related to anterior corneal curvature at a constant ratio. Previous studies have shown that the magnitude of posterior corneal astigmatism is related to the magnitude of anterior corneal astigmatism, and that the steep meridian of the posterior cornea is vertically aligned in most eyes. Thus, we propose that total corneal astigmatism can be estimated under the assumption that the magnitude of posterior corneal astigmatism is related to the magnitude of anterior corneal astigmatism at a constant ratio. We hypothesized that using an estimation of posterior corneal astigmatism from anterior corneal measurements based on the anterior-to-posterior corneal cylinder power ratio provides more accurate measurement of corneal astigmatism and will improve prediction of corneal astigmatism correction by toric IOLs compared to using simulated keratometry (SimK).

This study introduces a method to calculate estimated total corneal astigmatism using the anterior-to-posterior corneal cylinder power ratio according to the axis orientation of anterior corneal astigmatism. The aim of this study was to investigate the accuracy of a Sub–toric IOL calculator that predicts residual astigmatism and corneal plane effective cylinder power of toric IOLs based on effective lens position with estimated total corneal astigmatism using the anterior-to-posterior corneal cylinder power ratio according to the axis orientation of anterior corneal astigmatism.

## Methods

## Study Population

This retrospective cross-sectional study was conducted at the Department of Ophthalmology, Korea University College of Medicine. The study included 928 eyes of 928 reference subjects and 20 eyes of 20 cataract patients. The Institutional Review Board of Korea University Ansan Hospital, Gyeonggi, Korea, approved this study. All research and data collection adhered to the tenets of the Declaration of Helsinki.

Retrospective reviews were performed on all subjects who underwent a single Scheimpflug camera examination (Pentacam; Oculus Optikgeräte, Wetzlar, Germany) at our institution between May 1, 2009 and January 31, 2015. Reference subjects were selected after reviewing their electronic medical records and single Scheimpflug examination results. Subjects 30 years of age or older were included. Eyes that had previously undergone ocular surgery, that had corneal disease (such as keratoconus) or other corneal pathology that could affect Scheimpflug measurements, or that had been subjected to contact lens use within the 3 weeks prior to measurements were excluded. In cases where both of the patient’s eyes met the inclusion criteria, the eye with the more regular topographic pattern according to Scheimpflug measurements was enrolled at the discretion of a single examiner (Y.E.).

A total of 20 eyes from 20 cataract patients who underwent uncomplicated phacoemulsification with toric IOL (TECNIS 1-piece toric ZCT00; Abbott Medical Optics, Santa Ana, California, USA) implantation at our institute between July 1, 2013 and January 31, 2015 were enrolled. Cataract patients who underwent postoperative measurements with a single Scheimpflug camera and anterior segment photographs that showed the location of the anterior cylinder axis marks of the toric IOL were included. Eyes with axis differences less than 5 degrees between the anterior cylinder axis marks of toric IOLs and the steep meridians of anterior corneal astigmatism were included. Patients with a best-corrected visual acuity (BCVA) <20/40 in the operated eye, irregular corneal astigmatism, traumatic cataracts, previous ocular surgery, complicated cataract surgery, or postoperative complications were excluded.

## Patient Examination

In 928 reference subjects, the steep and flat radii and the flat axes of the anterior and posterior corneal surfaces were measured using a single Scheimpflug camera. For a single Scheimpflug measurement, scans with good quality states (according to the quality status mark displayed on Pentacam maps) for both anterior and posterior corneal measurements were selected for subject analysis.

In 20 cataract patients, preoperative corneal power, anterior chamber depth (ACD), and axial length (AL) were measured using an IOLMaster (version 5.02 or later; Carl Zeiss Meditec, Jena, Germany). IOL power was calculated using the Haigis formula (a _{0 }= −1.302, a _{1 }= 0.210, and a _{2 }= 0.251). Toric IOL cylinder power and axis were calculated using an online toric IOL calculator with an expected incision-induced astigmatism value of 0.30 diopter (D). After cataract surgery, postoperative BCVA, manual refractive error, and corneal radii were measured postoperatively between 4 and 12 weeks. After pupil dilation, an anterior segment photograph was taken to record the toric axis marks. The toric IOL axis as visualized in anterior segment photography was calculated using the angle tools in ImageJ (1.43u, rsb.info.nih.gov/ij/ ; National Institutes of Health, Bethesda, Maryland, USA).

## Surgical Technique

Preoperatively, the corneal limbus was marked at the 3-, 6-, and 9 o’clock positions using a Pre-Op Toric Reference Marker (AE-2793S; ASICO, Westmont, Illinois, USA) in the upright position under topical anesthesia with 0.5% proparacaine hydrochloride (Paracaine; Hanmi Pharmaceutical, Seoul, South Korea). All phacoemulsifications and toric IOL implantations were performed by 1 of 2 experienced surgeons (Y.E. or S.W.K.). A 2.75-mm clear corneal incision was made at the temporal cornea. A continuous curvilinear capsulorrhexis (slightly smaller than the IOL optic size) was then created with a 26 gauge needle. A standard phacoemulsification technique was used. The intraoperative alignment axis was marked using a Mendez degree gauge (AE-2765N; ASICO) and a Nuijts toric axis marker (AE-2740N; ASICO). The IOL was inserted into the capsular bag using a model 1MTEC30 cartridge (Abbott Medical Optics). After ophthalmic viscosurgical device removal, the toric IOL was rotated to the final position and verified using alignment axis marks.

## Main Outcome Measures

## Assessment of Corneal Astigmatism

Among 928 reference subjects, eyes were divided into 3 subgroups according to the axis orientation of anterior corneal astigmatism (with-the-rule [WTR], oblique, and against-the-rule [ATR] astigmatism). The relationship between SimK cylinder and posterior corneal cylinder power in each subgroup was analyzed using the linear regression equation Cyl _{Post }= β _{0 }+ β _{1 }× Cyl _{SimK }, where Cyl _{Post }is posterior corneal cylinder power, β _{0 }is the intercept parameter, β _{1 }is the slope parameter, and Cyl _{SimK }is simulated keratometry cylinder. β _{0 }and β _{1 }estimates for each subgroup were used to estimate posterior corneal astigmatism from anterior corneal measurements in 20 cataract patients. WTR astigmatism was defined as a flat meridian of the corneal surface of 180 ± 30 degrees, ATR astigmatism was defined as 90 ± 30 degrees, and all others were defined as oblique astigmatism.

## Postoperative residual astigmatism

In 20 cataract patients, postoperative residual astigmatism was defined as corneal plane ocular astigmatism measured through manual refraction at postoperative visits between 4 and 12 weeks.

## Predicted residual astigmatism

Predicted residual astigmatism was defined as the vectorial difference between corneal astigmatism and predicted corneal plane toric IOL astigmatism using vector analysis.

*Corneal astigmatism: *Calculations of predicted residual astigmatism were completed using 2 methods. One method used postoperatively measured SimK astigmatism, which was measured according to the conventional keratometer method using a refractive index of 1.3375. The other method used estimated total corneal astigmatism, which is defined as the vectorial sum of estimated posterior corneal astigmatism and anterior corneal astigmatism using a refractive index of 1.376. The linear regression results from 928 subjects were used to define estimated posterior corneal astigmatism. When linear regression outcome was statistically significant, estimated posterior corneal astigmatism was defined as follows:

where CA

_{Est_Post }is estimated posterior corneal astigmatism, β

_{0 }and β

_{1 }are parameters in the linear regression analysis of each reference subject subgroup, and Cyl

_{SimK }is the simulated keratometry cylinder. When regression analysis was not significant, estimated posterior corneal astigmatism was defined as the negative value of the mean posterior corneal astigmatism of a subgroup @ 90. The steep meridian of the posterior cornea was assumed to be 90 degrees, and cylinder axis marks on toric IOLs were assumed to be accurately placed at the steep meridian of the corneal astigmatism.

*Corneal Plane Effective Cylinder Power of Toric Intraocular Lenses: *The refractive vergence formula below was used to calculate the predicted corneal plane effective cylinder power of toric IOLs using corneal power and effective lens position :

D C o r n e a = 1336 1336 1336 1336 K 0 − E L P + D I O L + E L P − K 0