## Highlights

- •

A large preoperative lens vault may lead to hyperopic refractive outcomes.

- •

In eyes with a large lens vault, traditional formulas that include the preoperative anterior chamber depth in the calculation showed larger prediction errors.

- •

The Barrett and Kane formulas were less affected by lens vault and showed better accuracy than traditional formulas.

## Purpose

To explore the impact of preoperative lens vault (LV) on the accuracy of the Barrett Universal Ⅱ, Haigis, Hoffer Q, Hoffer QST, Holladay 1, Kane, and SRK/T formulas in eyes with a shallow anterior chamber.

## Design

Retrospective case series.

## Methods

Included were 409 eyes with anterior chamber depth (ACD) shallower than 3.0 mm that underwent phacoemulsification. Eyes were divided into a short axial length (AL) group (<22.00 mm) and a normal AL group (22.00 ≤ AL < 24.50 mm). Each group was further divided into a small LV subgroup (LV <0.95 mm) and a large LV subgroup (LV ≥0.95 mm) according to the median of the preoperative LV. Postoperative refraction was measured 3 months after surgery. Mean absolute error (MAE) was calculated and compared for each formula. The correlation between LV and the mean numeric error predicted by each formula was analyzed.

## Results

Overall, the Barrett and Kane formulas generated the smallest MAE in both short AL and normal AL groups ( *P* < .05 for both). In short AL eyes with small LV, the Haigis formula performed better than other traditional formulas ( *P* < .05 for all). In normal AL eyes with a small LV, the Barrett and Kane formulas showed higher accuracy ( *P* < .05 for all), and other formulas were comparable. In either subgroup with a large LV, the Haigis formula created a significant higher MAE ( *P* < .001 for all), followed by Hoffer QST. Positive correlations were found between LV and mean numeric errors predicted by all formulas, except for Barrett and Kane formulas ( *P* < .001 for all), indicating a postoperative hyperopic shift with an increased LV.

## Conclusions

In shallow anterior chamber eyes with a large LV, the Haigis and Hoffer QST formulas taking preoperative ACD into calculation surprisingly showed a larger prediction error. However, the Barrett and the Kane formulas, which include both ACD and lens thickness as predictive parameters, showed good accuracy in both small and large LV subgroups. Therefore, although formulas referring to preoperative ACD are generally believed to achieve better refractive results in patients with a shallow anterior chamber, LV may be valuable to consider when choosing an IOL power calculation formula.

W w ith the rapid development of phacoemulsification and intraocular lens (IOL) technology in recent years, cataract surgery has entered an era where refractive results are equally significant. Patients with a shallow anterior chamber usually undergo cataract surgery earlier than others due to the accompanying narrow angle, increased intraocular pressure (IOP), or hyperopia. For this reason, these patients may have higher expectations for postoperative visual outcomes. However, errors in IOL power prediction are significantly larger in eyes with a shallow anterior chamber, which lead to more inaccurate postoperative refraction. Therefore, choosing the most appropriate formula to calculate IOL power is clinically significant in such cases.

The effective lens position (ELP) is an important factor that determines the refractive power of the IOL, which, however, is not measurable before surgery and can only be predicted based on preoperative ocular biometrics. Third-generation formulas such as Hoffer Q, Holladay 1, and SRK/T ^{,} use corneal power and axial length (AL) to predict ELP. Haigis, a fourth-generation formula, uses AL and preoperative anterior chamber depth (ACD), measured from corneal epithelium to lens instead of corneal power.

Nowadays, several new-generation formulas have been created to improve the accuracy of IOL power predictions. Among them, the Barrett Universal Ⅱ (hereinafter referred to as Barrett) and Kane formulas have been considered to be the most accurate in all AL ranges. In the Barrett formula, lens thickness (LT) and white-to-white (WTW) distance are also recommended as optional variables in addition to corneal power, AL, and ACD. AL, corneal power, ACD, and sex are required for calculation in the Kane formula, with LT and central corneal thickness (CCT) as optional parameters. In addition to theoretical optics, the Kane formula integrates regression and artificial intelligence to improve its prediction. The Hoffer QST formula was recently created to refine the accuracy of the Hoffer Q formula by adding ACD as a variable and integrating artificial intelligence into the calculation.

Preoperative ACD is one of the significant predictors of ELP ^{,} and has been suggested as a factor of consideration in choosing the IOL calculation formula. ^{,} However, which formula should be selected in eyes with a shallow anterior chamber remains controversial. A previous study of eyes with a short AL and small ACD found the Haigis formula was more accurate, whereas other studies found that the Haigis formula—despite taking the preoperative ACD into calculation—showed the largest prediction error in shallow anterior chamber eyes. ^{,} Previous studies showed that in shallow ACD eyes, the Barrett formula was superior to traditional formulas, ^{,} while the Kane formula performed even better than the Barrett formula.

In addition to congenital anatomical factors, lens-related factors as another important mechanism causing shallow anterior chamber diseases have attracted more and more attention. Previous studies have shown that lens vault (LV)—an indicator of the position of the lens—is closely related to refractive outcomes after cataract surgery in shallow anterior chamber cases. ^{,} However, there is currently a lack of research on the effect of LV on the choice of the IOL calculation formula. Therefore, the purpose of this study was to compare the accuracy of the IOL formulas in groups subdivided by LV and to explore the effect of LV on postoperative refraction.

## METHODS

This retrospective case series included 409 shallow anterior chamber eyes (ACD <3.0 mm) of 409 consecutive patients who underwent uncomplicated phacoemulsification with implantation of the Tecnis ZCB00 IOL (Johnson & Johnson Vision) by one surgeon at the eye center of the Second Affiliated Hospital of Zhejiang University from January 2018 to June 2019. The exclusion criteria included previous ocular operations (with the exception of laser peripheral iridotomy, which does not affect ACD, LV, or ELP ^{,} ), corneal diseases, combined surgical procedures during cataract surgery, and eyes with incomplete data. Patients with postoperative best corrected visual acuity (BCVA) of <20/40 were also excluded to ensure the accuracy of refractive measurements. If both eyes of a participant met the inclusion criteria, only one of the eyes was randomly selected via the random number table to reduce interference in the correlation study. The research adhered to the tenets of the Declaration of Helsinki. The Ethics Committee of the Second Affiliated Hospital of Zhejiang University approved the protocol and waived informed consent.

Each patient underwent a standard preoperative ophthalmic examination, including slitlamp microscopy, ophthalmoscopy, BCVA, subjective refraction, IOP measurement, and gonioscopy. Measurements of the preoperative AL, corneal power, ACD, WTW, and LT were performed using a swept-source optical coherence tomography-based instrument (IOLMaster 700, Carl Zeiss). Only high-quality images with good central reflection and high-resolution scleral spurs were included in data analysis.

The preoperative LV was defined as the vertical distance from the most anterior point of the crystalline lens to the line connecting the scleral spurs and was measured and recorded on the cross-sectional horizontal scans obtained with an anterior segment optical coherence tomography (ASOCT; Visante, Carl Zeiss) before surgery ( Figure 1 ). CCT was also measured with ASOCT. The required refractive power of the IOL was calculated using the IOLMaster 700 software based on the optimized IOL constants given by the User Group for Laser Interference Biometry.

All operations were performed by one specialist (K.Y.) according to the standard protocol under topical anesthesia. A 2.0-mm corneal microincision was made, followed by continuous curvilinear capsulorrhexis and hydrodissection. After the lens was phacoemulsified and completely aspirated, a one-piece foldable IOL (ZCB00) was inserted into the capsular through a non-preloaded IOL injector (Viscoject-Bio, Medicel AG) with wound-assisted technique.

Subjective refraction was examined at 3 months postoperation. Mean absolute error (MAE), defined as the absolute value of the difference between the actual and expected refractive error after surgery, was considered as a main outcome in reflecting the accuracy of IOL power prediction for each formula. Other main outcomes included the median absolute error and percentage of eyes within ±0.25 diopters (D), ±0.50 D, and ±1.00 D of predicted refraction.

According to the updated IOL Power Calculation Study Protocols, the Haigis, Hoffer Q, Holladay 1, and SRK/T formulas were calculated with optimized IOL constants for the whole population given by the User Group for Laser Interference Biometry. The Barrett, Hoffer QST, and Kane formulas were calculated through their respective online calculators with the recommended constants. Lens constants used in this study were A-constant of 119.39 for Barrett, personalized (p)ACD of 5.80 for Hoffer Q, pACD of 5.85 for Hoffer QST, surgeon factor of 2.02 for Holladay 1, A-constant of 119.36 for Kane, and A-constant of 119.30 for SRK/T. For Haigis, a0 = −1.302, a1 = 0.210, and a2 = 0.251.

Previous studies have shown that the choice of the IOL calculation formula should take AL into consideration. For this reason, the entire population was divided into the short AL group (<22.00 mm) and the normal AL group (22.00 to 24.50 mm). Only two patients in this population had an AL > 24.50 mm, so they were excluded from the data analysis. To investigate the effect of LV on MAE prediction for each formula, the median LV of the total population (0.95 mm) was set as the cutoff value for further subgroup division.

## STATISTICAL ANALYSIS

SPSS 21 (IBM Corp) and Microsoft Excel (Microsoft Inc) software were used for statistical analysis. The Friedman test and post hoc multiple comparisons with Bonferroni correction were used to compare the prediction accuracy between the formulas. The correlation between LV and predicted refractive error was evaluated by the Pearson correlation test. A *P* value of <.05 was considered significant.

## RESULT

This study retrospectively analyzed the clinical data from 409 eyes of 409 patients eligible for the inclusion criteria. Baseline clinical characteristics and ocular biometrics of all participants are summarized in Table 1 . The patients were a mean age of 67.99 ± 10.77 years, of which 71.9% (294/409) were women. The mean preoperative BCVA was 0.48 ± 0.31 logMAR, with a mean refractive error of 0.75 ± 1.76 D. The mean AL was 22.69 ± 0.79 mm, the mean corneal power was 44.24 ± 1.88 D, the mean ACD was 1.99 ± 0.22 mm, and the mean LV was 0.95 ± 0.20 mm. The mean power of the implanted IOL was 22.23 ± 1.89 D.

Characteristics | Mean ± SD or No. (%) | Range |
---|---|---|

(N = 409) | ||

Age, y | 67.99 ± 10.77 | 42-91 |

Female sex | 294 (71.8) | — |

Right laterality | 202 (49.4) | — |

Refractive error, D | 0.75 ± 1.76 | −6.00 to 4.00 |

BCVA, logMAR | 0.48 ± 0.31 | 0.10-1.70 |

Intraocular pressure, mm Hg | 15.93 ± 3.56 | 10.0-28.5 |

Axial length, mm | 22.69 ± 0.79 | 20.40-24.43 |

Corneal power, D | 44.24 ± 1.88 | 40.89-48.50 |

Anterior chamber depth, mm | 1.99 ± 0.22 | 1.55-2.49 |

Lens vault, mm | 0.95 ± 0.20 | 0.39-1.49 |

Intraocular lens power, D | 22.23 ± 1.89 | 18.0-28.0 |

Table 2 summarizes the comparison of the MAE and median absolute error generated by the seven formulas in subgroups of different AL. The Barrett and Kane formulas achieved the most accurate prediction in both the short AL group and the normal AL group ( *P* < .05 for all). In the short AL group (AL < 22.0 mm), the Hoffer Q and Hoffer QST generated the smallest MAE (0.45 D and 0.44 D, respectively), with a significant difference from other traditional formulas ( *P* < .05 for all). No significant difference of the MAE was found between other formulas. In the normal AL subgroup (22.00 to 24.50 mm), the MAEs predicted by the Haigis formula (0.46 D) were significantly higher than the other formulas ( *P* < .001 for all), whereas the Holladay 1, SRK/T, Hoffer Q, and Hoffer QST formulas showed similar accuracy in IOL power prediction.

Axial Length, mm | Barrett | Haigis | Hoffer Q | Hoffer QST | Holladay 1 | Kane | SRK/T | Post Hoc ^{a } |
---|---|---|---|---|---|---|---|---|

<22.0 mm (n = 70) | ||||||||

ME, D | −0.02 | −0.13 | −0.15 | −0.13 | −0.13 | −0.01 | −0.16 | Kane = Barrett > Hoffer QST = Hoffer Q > SRK/T = Holladay 1 = Haigis |

MAE ± SD, D | 0.34 ± 0.23 | 0.49 ± 0.34 | 0.45 ± 0.35 | 0.44 ± 0.35 | 0.48 ± 0.41 | 0.32 ± 0.25 | 0.47 ± 0.37 | |

MedAE, D | 0.32 | 0.41 | 0.39 | 0.40 | 0.42 | 0.28 | 0.40 | |

±0.25 D, n (%) | 29 (41.4) | 20 (28.6) | 23 (32.9) | 23 (32.9) | 20 (28.6) | 30 (42.9) | 23 (32.9) | |

±0.5 D, n (%) | 51 (72.9) | 39 (55.7) | 39 (55.7) | 41 (58.6) | 38 (54.3) | 52 (74.3) | 43 (61.4) | |

±1.00 D, n (%) | 66 (94.3) | 58 (82.8) | 62 (88.6) | 63 (90.0) | 60 (85.7) | 67 (95.7) | 64 (91.4) | |

>±2.00 D, n (%) | 0 (0) | 0 (0) | 0 (0) | 0 (0) | 0 (0) | 0 (0) | 0 (0) | |

22.0-24.49 mm (n = 339) | ||||||||

ME, D | 0.00 | −0.06 | −0.07 | −0.07 | −0.02 | 0.00 | 0.03 | Kane = Barrett > SRK/T = Holladay 1 = Hoffer Q = Hoffer QST > Haigis |

MAE ± SD, D | 0.31 ± 0.25 | 0.46 ± 0.32 | 0.39 ± 0.33 | 0.40 ± 0.33 | 0.38 ± 0.36 | 0.30 ± 0.23 | 0.36 ± 0.30 | |

MedAE, D | 0.22 | 0.37 | 0.30 | 0.32 | 0.29 | 0.23 | 0.26 | |

±0.25 D, n (%) | 146 (43.1) | 100 (29.5) | 128 (37.8) | 130 (38.3) | 130 (38.3) | 149 (44.0) | 137 (40.4) | |

±0.5 D, n (%) | 257 (75.8) | 187 (55.2) | 226 (66.7) | 220 (64.9) | 230 (67.8) | 261 (77.0) | 238 (70.2) | |

±1.00 D, n (%) | 334 (98.5) | 301 (88.7) | 323 (95.3) | 319 (94.1) | 324 (95.6) | 335 (98.8) | 324 (95.6) | |

>±2.00 D, n (%) | 0 (0) | 0 (0) | 0 (0) | 0 (0) | 0 (0) | 0 (0) | 0 (0) |