## Purpose

To investigate the effect of a modified Haigis formula effective lens position equation on improving refractive outcomes in eyes with ciliary sulcus–implanted intraocular lenses (IOLs).

## Design

Retrospective cross-sectional study.

## Methods

One hundred thirty-two eyes of 132 consecutive patients who underwent phacoemulsification with implantation of a ZA9003 (Abbott Medical Optics Inc, Santa Ana, California, USA; 69 eyes) or AR40e (Abbott Medical Optics Inc; 63 eyes) IOL in the ciliary sulcus were enrolled. The modified effective lens position (ELP) equation based on the corneal radius (CR) (ELP − β _{0 }− β _{1 }× CR, where β _{0 }and β _{1 }are parameters in the linear regression analysis) was obtained using linear regression analysis in each IOL group, and was applied to the other IOL group in order to evaluate its effect on refractive outcomes in an independent data set. The median absolute error (MedAE) was predicted using the modified effective lens position equation and was compared with that predicted using the adjusted IOL power.

## Results

The modified effective lens position equation was ELP + 11.662 − 1.6225 × CR in the ZA9003 group and ELP + 10.606 − 1.4817 × CR in the AR40e group. The MedAE that was predicted using the modified effective lens position equation (0.34 diopter [D] in the ZA9003 group and 0.42 D in the AR40e group) was significantly smaller than that predicted using the adjusted IOL power (0.47 D in the ZA9003 group and 0.66 D in the AR40e group) ( *P *< .001 and *P *= .005, respectively).

## Conclusions

IOL power calculation using the modified Haigis formula effective lens position equation improved refractive outcomes in eyes with sulcus-implanted IOLs.

Modern cataract surgery has allowed for greatly improved postoperative vision owing to more advanced surgical techniques, improved intraocular lens (IOL) power formulas, and the advent of precise biometry techniques. Despite advances in surgical techniques, intraoperative complications can still occur, and a posterior capsule tear is the most common serious complication during cataract surgery. Placement of a 3-piece IOL in the ciliary sulcus is a common treatment option for posterior capsule rupture. The effective lens position of the sulcus-implanted IOL is smaller than that of the predicted effective lens position for the in-the-bag IOL because the sulcus-implanted IOL is located anterior to the in-the-bag IOL. Thus, the sulcus-implanted IOL needs less power to achieve a similar postoperative refraction to the in-the-bag IOL. Previous studies have shown that a reduced sulcus-implanted IOL power can provide better refractive outcomes than IOL power for in-the-bag implantation.

A previous study demonstrated that sulcus-implanted IOLs provided good postoperative corrected visual acuity when compared to in-the-bag IOLs. Therefore, uncorrected distance visual acuity (UDVA) can be improved by more accurate predictions of the postoperative refraction of a sulcus-implanted IOL. Previous studies have attempted to improve refractive outcomes in eyes with corneal power (keratometry [K]) or axial length (AL) deviated from the average value. However, the postoperative refraction of eyes with sulcus-implanted IOLs is usually roughly estimated by reducing the IOL power at the surgeon’s discretion. Dubey and associates demonstrated that adjustment of IOL power according to the AL and predicted IOL power can reduce unexpected refractive error, but this only roughly estimated postoperative refraction. We wanted to more accurately predict postoperative refraction in eyes with sulcus-implanted IOLs. More accurate IOL power calculation may be possible in eyes with a sulcus-implanted IOL if their effective lens position is predicted using constants from IOL power calculation formulas instead of using the effective lens position of the in-the-bag IOL. This study introduces a method to calculate sulcus-implanted IOL power using a modified Haigis formula effective lens position equation and modified Haigis constants. The aim of this study was to investigate the effect of a modified Haigis formula effective lens position equation on improving refractive outcomes in eyes with sulcus-implanted IOLs.

## Methods

## Study Population

This retrospective cross-sectional study included 132 eyes from 132 consecutive patients who underwent phacoemulsification with implantation of a Tecnis ZA9003 (Abbott Medical Optics Inc, Santa Ana, California, USA; 69 eyes) or a Sensar AR40e (Abbott Medical Optics Inc; 63 eyes) IOL in the ciliary sulcus owing to posterior capsule rupture during cataract surgery at Korea University College of Medicine between March 3, 2008 and May 29, 2015. We included patients who had a best-corrected visual acuity (BCVA) greater than 20/40 in the operated eye after cataract surgery. Patients with traumatic cataracts, a history of previous ocular surgery (eg, penetrating keratoplasty and refractive surgery), scleral-fixated IOLs, optic-captured IOLs, IOL exchanges, postoperative complications, indwelling silicone oil, and prior retinal detachment were excluded. Eyes with medical records indicating noticeable postoperative IOL tilt or decentration were also excluded. The institutional review boards of Korea University Anam Hospital (Seoul, South Korea), Korea University Guro Hospital (Seoul), and Korea University Ansan Hospital (Gyeonggi, South Korea) approved the present study. All research and data collection adhered to the tenets of the Declaration of Helsinki.

## Patient Examination

Preoperative K, corneal radius, anterior chamber depth (ACD) from the corneal epithelium to the anterior surface of the crystalline lens, and AL were measured using an IOLMaster (Carl Zeiss Meditec, Jena, Germany; version 5.02 or higher). Postoperative UDVA, subjective refraction, and BCVA were measured at visits between 3 and 10 weeks after surgery.

## Surgical Technique

Phacoemulsification with IOL implantation was performed under topical anesthesia with 0.5% proparacaine hydrochloride (Alcaine; Alcon Laboratories Inc, Fort Worth, Texas, USA or Paracaine; Hanmi Pharm, Seoul, Korea). A 2.2 mm or 2.75 mm clear corneal incision was made at the temporal cornea. A continuous curvilinear capsulorrhexis (CCC) slightly smaller than the IOL optic size was then created with a 26 gauge needle. A standard phacoemulsification technique was used. After the posterior capsule ruptured, the most appropriate means for removing residual lens material was determined at the discretion of the individual operating surgeon. Anterior vitrectomy was performed to remove prolapsed vitreous from the anterior chamber. In patients with a 2.2 mm clear corneal incision, the incision was enlarged to 2.8 mm. IOL power reduction was determined by the individual surgeon based on the results of previous studies. In patients with an intact CCC or sufficient anterior capsule support, the IOL was inserted into the ciliary sulcus using an UNFOLDER Emerald T Handpiece with an Emerald C cartridge (Abbott Medical Optics Inc). In some cases, a corneal suture was placed at the discretion of the surgeon.

## Main Outcome Measure(s)

The median absolute error (MedAE) was defined as the median absolute value of the refractive prediction error. The refractive prediction error was defined as the difference between the refractive spherical equivalent observed 3–10 weeks after surgery and the preoperative predicted refraction determined using the Haigis formula (refractive prediction error = postoperative spherical equivalent − preoperative predicted refraction). The Haigis formula IOL constants a _{0 }, a _{1 }, and a _{2 }were −1.298, 0.233, and 0.240, respectively, in the ZA9003 group and 2.420, 0.157, and 0.288, respectively, in the AR40e group (Optimized IOL Constants for the *ZEISS IOLMaster *. Available at http://www.augenklinik.uni-wuerzburg.de/ulib/c1.htm . Accessed May 1, 2015).

The preoperatively estimated effective lens position was calculated using a regression equation from the Haigis formula, as follows :

E L P = a 0 + a 1 × A C D + a 2 × A L

*ELP*is effective lens position;

*a*

_{0 },

*a*

_{1 }, and

*a*

_{2 }are IOL constants for the Haigis formula;

*ACD*is anterior chamber depth; and

*AL*is axial length.

## Adjustment of Intraocular Lens Power

A previous study recommended that the IOL power be reduced by 1.0 diopter (D) for eyes with a predicted IOL power ranging from 18.0 to 25.0 D and by 1.5–2.0 D for eyes with a predicted IOL power greater than 25.0 D. However, when an IOL with reduced power is implanted in the ciliary sulcus, postoperative refraction is predicted for the in-the-bag IOL using the IOL power calculation formula. We investigated the effects of IOL power adjustment on the refractive outcomes of sulcus-implanted IOLs, based on the predicted IOL power. The predicted refraction for a sulcus-implanted IOL is assumed to be the predicted refraction for an in-the-bag IOL plus the amount of adjusted IOL power, as determined above. Preoperative predicted refraction was determined to be the predicted refraction of 0.5 D greater IOL power for IOLs <18.0 D; 1.0 D greater IOL power for IOLs from 18.0 to 25.0 D; and 1.5 D greater IOL power for IOLs >25.0 D.

## Optimization of Haigis Constants

The data-adjusted a _{0 }, a _{1 }, and a _{2 }constants for the Haigis formula were calculated with linear regression analysis using the back-calculated effective lens position (see below) in order to obtain zero mean arithmetic error in the sulcus-implanted IOL power prediction. We used regression analysis to identify correlations between K and the optimized refractive prediction error based on the data-adjusted IOL constants.

The back-calculated effective lens position was defined as the postoperatively calculated effective lens position based on preoperative K, AL, sulcus-implanted IOL power, and postoperative refraction. The back-calculated effective lens position was obtained using the following thin lens formula:

I O L p o w e r = n × 1000 A L − E L P − n × 1000 n × 1000 Z − E L P