**1. Introduction**

The accurate calculation of intraocular lens (IOL) power is critical for providing optimal visual acuity results for cataract surgery patients. As axial lengths reach the extremes, the variation in outcomes increases significantly, demonstrating the need to carefully select the best formula [1–3]. The first-generation SRK I, second-generation SRK II, and Hoffer formulas have given way to the more modern third-generation Holladay 1, Hoffer Q, and SRK/T formulas, as well as the fourth-generation Haigis and Barrett Universal II (BU-II) formulas [3,4]. The SRK/T formula, in particular, has been shown to be particularly accurate in eyes with an AL ≥ 27.0 mm [5–7]. More recent formulas include the Hill–Radial Basis Function version 3.0, Emmetropia Verifying Optical (EVO), and Kane [7–9]. The resulting improvement in accuracy has increased the popularity of newer formulas among cataract surgeons [1,5,10].

Despite the increased accuracy of the newer third- and fourth-generation formulas, they tend to underestimate IOL power for patients with longer eyes, causing postoperative hyperopia [11]. An AL modification method, referred to as the Wang–Koch (WK) adjustment, was published by Wang et al. in 2017, which increases the accuracy of older generation formulas in patients with high AL [11]. Fernández et al. demonstrated that

**Citation:** Moshirfar, M.; Durnford, K.M.; Jensen, J.L.; Beesley, D.P.; Peterson, T.S.; Darquea, I.M.; Ronquillo, Y.C.; Hoopes, P.C. Accuracy of Six Intraocular Lens Power Calculations in Eyes with Axial Lengths Greater than 28.0 mm. *J. Clin. Med.* **2022**, *11*, 5947. https:// doi.org/10.3390/jcm11195947

Academic Editor: Nobuyuki Shoji

Received: 6 September 2022 Accepted: 2 October 2022 Published: 8 October 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

the variation in prediction error (PE) with axial length was due to considering a single refractive index and not due to errors in the prediction of effective lens position (ELP), suggesting a variation in the fictitious refractive index to address this problem [12]. In 2019, the Cooke-modified axial length (CMAL) method was proposed, which sums the individual ocular segmen<sup>t</sup> lengths to predict a sum-of-segments AL that improved the predictive power of third- and fourth-generation formulas in long and short eyes [13]. The addition of these methods increased the prediction accuracy of newer generation formulas such as SRK/T and Holladay in highly myopic eyes [5,14].

The BU-II formula was first presented as a modified version of the original Barrett formula in 2010; it is considered one of the most accurate but remains unpublished [5,9]. Other unpublished formulas include the EVO (Tun Kuan Yeo, MD), Kane (Jack Kane, MD), and Hill-RBF version 3.0 [9,15]. The Kane and Hill-RBF version 3.0 formulas both incorporate artificial intelligence to predict IOL power [7]. The newly updated Hill-RBF version 3.0 increased the database for eyes of all sizes, including myopic patients, and added central corneal thickness (CCT), lens thickness (LT), white-to-white (WTW), and gender to the existing parameters [15].

To our knowledge, the vast majority of studies evaluating the accuracy of the newer formulas in highly myopic patients have taken place with Asian participants, where high myopia is more common [16,17]. As eyes in Asian populations also tend to have flatter corneas, it is possible that the use of these formulas in other racial groups with longer axial lengths could have differing results [18,19]. Given this paucity of data outside of Asian populations, there is a need for studies of these newer formulas in highly myopic patients of non-Asian descent. The purpose of this study was to compare the IOL accuracy of six IOL power formulas for eyes with extremely long axial lengths ( ≥28.0 mm) from a predominantly Caucasian population.

#### **2. Materials and Methods**

#### *2.1. Subjects and Procedures*

This study was a retrospective review of consecutive cataract patients having undergone uncomplicated phacoemulsification procedures at a single site from January 2013 to May 2021. The Lenstar® LS 900 (Haag-Streit AG, Koeniz, Switzerland) reviewed 16,538 eyes and initially identified 71 records of patients with axial lengths > 28.0 mm who subsequently underwent simple phacoemulsification. Patients included had a manifest refraction performed at least one month postoperatively with a corrected distance visual acuity (CDVA) of 20/40 or better. Eyes with prior refractive surgery, intraoperative or postoperative cataract complications, a history of severe fundus pathology (e.g., myopic degeneration or macular hole), or a lack of postoperative refraction at one month or greater were excluded; this left 35 eyes of 25 patients for analysis (Figure S1). The data were de-identified prior to analysis.

Biometric measurements included AL, keratometry (K), anterior chamber depth (ACD, measured from the corneal epithelium to the lens), WTW, CCT, LT, and aqueous depth. Preoperative refraction, uncorrected distance visual acuity (UDVA), and CDVA were noted as well. All visual acuity measurements were converted to the equivalent logarithm of the minimum angle of resolution (LogMAR). Additionally, the patient's age, gender, and past ocular and medical history were included in the data analysis. The patient's self-reported ethnicity data were not recorded in the paper charts. Ethnicity was projected from the area's demographics and recent census data.

#### *2.2. Surgery and Intraocular Lenses*

The standard phacoemulsification procedure was performed on all the patients by a single experienced surgeon using topical anesthesia. One of six different foldable acrylic lenses was inserted into the eye. The models of IOL lens choices included the AR40e (Sensar ®, Johnson & Johnson Vision, Jacksonville, FL, USA), MA60MA (Alcon Laboratories, Fort Worth, TX, USA), MX60E (enVista ®, Bausch + Lomb, Rochester, NY, USA), ZCB00 (TECNIS ®, Johnson & Johnson Vision, Jacksonville, FL, USA), ZCT225 (TECNIS ®, Johnson

& Johnson Vision, Jacksonville, FL, USA), and ZXR00 (TECNIS Symfony®, Johnson & Johnson Vision, Jacksonville, FL, USA). Patients were instructed to use third- or fourthgeneration fluoroquinolone antibiotic eye drops four times daily for one week. Patients were also started on a topical steroid medication four times daily and tapered weekly over one month. A topical NSAID eye drop was used twice daily for six weeks. Patients were then scheduled for one-day, one-week, and one-month follow-up appointments where the LogMAR, UDVA, and intraocular pressure (IOP) were checked. At the one-month postoperative appointment, manifest refraction was performed, and LogMAR CDVA was recorded. Any additional follow-up appointments were recorded within two years; IOP, CDVA, UDVA, and manifest refractions were recorded for any of these follow-up visits. The last manifest refraction charted was recorded as the patient's postoperative spherical equivalent (SE) to analyze the prediction error.

#### *2.3. Retrospective and Statistical Analysis*

The six formulas evaluated were:


Due to the small study sample and evaluation of long eyes, IOL constants for the implanted lenses were obtained from those listed in the User Group for Laser Interference Biometry database (available at http://ocusoft.de/ulib/c1.htm, referred to as ULIB, accessed 15 June 2021). To calculate the predicted SEs, the ULIB IOL constants for each lens and the patient's biometric data were input into each formula. The published Holladay 1 and SRK/T formulas were exported directly into Excel (Microsoft Corporation, Redmond, WA, USA). The AL was adjusted for the Holladay 1 and SRK/T formulas using the modified regression WK adjustment and the CMAL adjustment, resulting in two iterations of each formula. For the remaining four unpublished formulas, ULIB IOL constants and biometrics were input into the online calculators via Python (Python Software Foundation, Wilmington, DE, USA) as recommended by Hoffer and Savini [22]. Refractive prediction errors (PE) were then calculated by subtracting the formula-predicted SE refractive error from the postoperative manifest refraction SE. Absolute prediction errors (AE) were calculated from the PE.

Mean prediction error (MPE) was used to assess for postoperative myopic or hyperopic surprises. As described by Hoffer and Savini, the mean absolute error (MAE) and median absolute error (MedAE) were calculated for each formula to assess the predictive accuracy [22]. The max AE was noted for each formula as well. The cases were analyzed by the percentage of eyes with a PE of ±0.25 diopters (D), ±0.50 D, ±0.75 D, and ±1.00 D for each formula. The postop refraction values were rounded to the closest step to account for the invariant refraction assumption.

Statistical analysis was performed using R version 4.0.2 (22 June 2020) statistical software. Continuous variables were reported with a mean and standard deviation (SD), and categorical variables were reported with a number and percentage. The normality of the data was assessed with the Shapiro–Wilk test. The distribution of the AE values did not follow normal Gaussian distribution, so nonparametric tests were used. The difference in refractive errors between formulas was assessed with the paired Wilcoxon signed-rank test. The percentages of PE within ±0.25 D, ±0.50 D, ±0.75 D, and ±1.00 D for each formula were compared with a Cochran's Q test. McNemar's test with Bonferroni adjustment was

then used to identify any statistically significant difference identified in the Cochran's Q. A *p*-value less than 0.05 was considered statistically significant.
