This study compared the refractive outcomes of nine IOL formulas in patients with APAC history. In APAC eyes, inferior predictability and myopic shift were observed compared to the control eyes. MedAEs were not statistically different in APAC eyes of AL ≥ 22 mm; however, in APAC eyes with AL < 22 mm, Haigis and Hill-RBF 3.0 showed the lowest MedAEs. Preoperative LPI did not affect the postoperative refractive outcomes in APAC eyes.

Previous studies using conventional IOL formulas reported that eyes with a history of PACG yield inaccuracy in refractive prediction [1, 7, 12,6,13,14]. Joo et al. [12] compared the refractive outcome after the cataract surgery in 63 eyes with APAC who received preoperative LPI and 93 eyes in the control group for three traditional formulas (Hoffer Q, SRK/T, and Haigis). The authors reported that Haigis showed inferior predictability (MAE, 0.69 ± 0.54 D) and Hoffer Q (MAE, 0.53 ± 0.39 D) showed superior outcomes than the others in PACG patients. A more hyperopic shift was observed in the SRK/T and Haigis formulas and a myopic shift in the Hoffer Q formula. Seo et al. [6] reported that among 193 PAC or PACG patients, Hoffer Q (0.44 ± 0.34 D) had the least MPE among Hoffer Q, Haigis (0.50 ± 0.37 D), and SRK/T (0.46 ± 0.34 D) formulas. A hyperopic shift was observed in all formulas. In contrast, Day et al. [8] reported that Haigis showed the lowest MAE (0.30 ± 0.20 D) and Hoffer Q showed the highest MAE (1.11 ± 1.32 D) among Hoffer Q, SRK/T, and Haigis formulas in the effectiveness in angle-closure glaucoma of lens extraction study (EAGLE) (N = 208), in line with this study’s results. Day et al.’s study observed a myopic shift for Hoffer Q and a hyperopic shift for SRK/T. Meanwhile, Lee et al. [1] reported that peripheral anterior synechia (PAS) is related to higher MAE and myopic shift regardless of IOL formulas, including SRK/T, Hoffer Q, Haigis, and Holladay.

There are several hypotheses regarding postoperative refractive outcomes in PAC or PACG patients. The myopic shift may be associated with a high anterior lens vault, defined as the perpendicular distance between the anterior pole of the lens and a horizontal line between the scleral spurs, resulting in an anteriorly positioned IOL after surgery [14, 15]. In contrast, hyperopic shift may also occur because cataract surgery yields deepening of the anterior chamber and IOL shift to a more posterior plane by removing the lens volume and the pupillary block component. Decreased AL because of IOP lowering also can contribute to hyperopic shift [6]. If PAS is present, PAS may interfere with ciliary body reposition and posterior shifting of the IOL plane, also resulting in myopic shift [1]. In this study, APAC eyes showed more myopic shift than control groups. We did not evaluate the preoperative lens vault using anterior segment optical coherence tomography, and the status of PAS was not accessed in all eyes, so the exact mechanism of myopic shift was not suggested in this study.

Efforts to improve the postoperative outcome of cataract surgery are in place with the development of various formulas, including artificial intelligence. New generation formulas such as BUII, Kane, or Hill-RBF 3.0 showed higher postoperative accuracy than the conventional formulas in cataractous eyes [16,17,18,19,20,21]. Until now, two studies by Hou et al. [7] and Ding et al. [11] analyzed accuracy using recent IOL formulas for primary angle-closure disease (PACD). Hou et al. evaluated the accuracy of seven IOL formulas (SRK/T, Haigis, Hoffer Q, BUII, Kane, Ladas super formula, and Hill-RBF 3.0) for the five different IOL models including ZCB00 (54%), MX60 (27.9%), SN60WF (13.2%), Aspira-aA (9.3%), and 970 C (7.8%). About two-thirds of the 129 eyes of 129 patients (N = 80) received additional glaucoma surgeries such as peripheral iridectomy and trabeculectomy in addition to cataract surgery. In their study, Kane and Hill-RBF 3.0 formulas performed better in new-generation formulas, while Haigis and SRK/T formulas showed better results in traditional formulas. The Kane formula showed the best accuracy in PACD with shorter AL (< 22 mm). On the contrary, Haigis and Hill-RBF 3.0 formulas showed better predictability in the APAC group in this study, while Hoffer Q, Kane, and Ladas super showed worse accuracy. In a study recently conducted by the same research group [11] compared six IOL formulas (BUII, Haigis, Hill-RBF 3.0, Hoffer Q, Kane, and SRK/T) in patients with PACD using single type of IOL and concluded that the standard deviation of Kane (0.59), Hill-RBF 3.0 (0.61) and SRK/T (0.62) were significantly lower than Hoffer Q (0.68). Study results of the two studies are somewhat different from ours: the formula showing the lowest standard deviation in the APAC group for our study was Haigis (0.67), followed by Hill-RBF 3.0 (0.69) which were slightly larger than those in the Ding et al.’s study and the percentage of eyes within PE ± 0.5 D was much higher (60.5 to 71.3%) in Hou’s study than those in APAC eyes in this study (45.5 to 56.8%). The difference may be related to the difference in ACD among the studies, which is shorter in Hou et al.’s study (2.22 ± 0.26 mm for no-surgery patients, 2.25 ± 0.35 mm for peripheral iridectomy patients, and 2.3 ± 0.32 mm for trabeculectomy patients) and Ding et al.’s study (2.21 ± 0.28 mm) than those in this study (2.43 ± 0.29 mm for eyes with AL < 22 mm and 2.46 ± 0.33 mm for eye with AL ≥ 22 mm).

AL and ACD are known to be important factors that affect the prediction of refractory outcomes. There have been many reports about IOL power calculation in short eyes [14, 15, 22,23,24,25,26,27]. In a study by Carmona-Gonzalez et al. [28], Haigis and EVO seem to be accurate when compared to the other ten formulas, including SRK/T, Hoffer Q, Holladay I, Holladay II, Haigis, Olsen, BUII, Hill-RBF, Ladas Super formula, and Kane. Eom et al. [23] reported that Haigis is more accurate than Hoffer Q when ACD was less than 2.40 mm. Shirvastava et al. [24] concluded that among seven formulas, Haigis showed the best outcome in short eyes with ACD greater than 2.40 mm (BUII, Haigis, Hill-RBF, Hoffer Q, Holladay I, Holladay 2, and SRK/T). This study also showed similar results to these studies. In the APAC group that showed short AL < 22 mm with shallow ACD (2.43 ± 0.29 mm), the Haigis showed the lowest MedAE values.

LPI relieves the pressure acting forward on the lens, resulting in the deepening of the central anterior chamber and backward positioning of the lens [29, 30]. Therefore, LPI may stabilize the effective lens position by deepening the ACD with the shortening of AL [13]. However, previous studies reported that ACD did not change after LPI [31, 32], and the effect of LPI on angle widening in APAC depends on PAS [30, 33]. This study also noted no statistical significance between those two groups, indicating that preoperative LPI does not benefit postoperative refractive outcomes. Further analysis with a larger cohort would be necessary to conclude the effect of LPI on postoperative refractive outcomes in APAC patients.

This study has some limitations. First, we did not clarify the angling status in all APAC patients. Of the 44 eyes in the APAC group, nine had no data of gonioscopy on preoperative status because they were transferred to our hospital from another clinic for cataract surgery after initial management, including LPI. The existence of PAS was difficult to evaluate in two eyes due to failure to relieve appositional obstruction of the trabecular meshwork during gonioscopy with indentation. Only one eye had PAS in the APAC group. The existence of PAS may induce higher MAE and more myopic shift, a lower proportion of PAS in this study would be considered when interpreting the results [6]. Second, only Asian patients were included in this study. Because there are ethnic differences in corneal curvature, anterior chamber angle, and AL [34], further study would be necessary to expand this study’s results in patients of other ethnicities. Third, while measuring the refraction by subjective refraction is the gold standard, the refractive error of the patients was measured with an auto-refractokeratometer. Fourth, LT or central corneal thickness may contribute to the accuracy of the formula [35, 36], these parameters were not considered in this study. Fifth, we could not fully optimize the lens constants for every formula since the status of APAC eyes, including ACD and ACD/AL ratio, is quite different from each other, and the study results were summed of three experienced but different surgeons. Further study using optimized lens constant for APAC patients calculated from a large cohort would be necessary.

In conclusion, compared to the control eyes APAC eyes showed myopic refractive outcomes. Haigis and Hill-RBF 3.0 showed high precision in the eyes with AL < 22 mm in the APAC group. None of the formulas shows statistically superior refractive outcomes in eyes with AL ≥ 22.0 mm in the APAC patients.