Clinical Accuracy of 6 Intraocular Lens Power Calculation Formulas in Elongated Eyes, According to Anterior Chamber Depth


To investigate the influence of anterior chamber depth (ACD) on the accuracy of the Kane, EVO 2.0, Barrett Universal II (BU II), Olsen, SRK/T, and Haigis formulas in patients with elongated eyes.


Retrospective case series study.


A total of 106 patients (106 eyes) diagnosed with high myopia (axial length ≥26 mm) were enrolled and divided into 3 subgroups according to preoperative ACD. Mean refractive error (ME), mean absolute refractive error (MAE), median absolute refractive error (MedAE), and proportions of eyes within ±0.25 D, ±0.50 D, ±0.75 D, and ±1.00 D were calculated.


In all patients, the MedAE was lowest for the Kane formula (0.28 D), followed by the BU II (0.34 D). In the shallow ACD subgroup, EVO 2.0 formula produced the lowest MedAE (0.22 D), and the highest proportion of eyes within ±0.25 D (58%); the BU II (0.23 D, 50%) and Kane (0.25 D, 50%) formulas produced similar proportions. In the deep ACD group, the MedAEs of the Haigis and SRK/T formulas (0.68 D and 0.50 D, respectively) were significantly higher than those of the EVO 2.0 (0.37 D), Kane (0.30 D), BU II (0.43 D), and Olsen (0.34 D) formulas ( P < 0.05).


Overall, the Kane and EVO 2.0 formulas had the highest accuracy. EVO 2.0 and BU II formulas are recommended for patients with shallow ACD; the Kane formula is recommended for patients with deep ACD (especially patients with extremely elongated eyes). The SRK/T and Haigis formulas should be avoided as much as possible.

A ccording to a 2016 epidemiological survey , approximately 163 million people worldwide exhibit high myopia; this number is expected to increase to 938 million (9.8% of the global population) by 2050. In 2018, the prevalence of high myopia in Asia ranged from 10% to 20% of all myopic people. Notably, the risk of high myopia−associated pathological changes increases with increasing axial length (AL). When the AL increases from 28.0 mm to 32.0 mm, the incidence of posterior scleral staphyloma increases from 5% to 50%. In addition, premature vitreous degeneration and increases in anterior chamber depth (ACD) and lens thickness (LT) cause reductions in the accuracies of various existing intraocular lens (IOL) power calculation formulas.

Thus far, most IOL formulas widely used in clinical practice are vergence formulas, which use 2 to 7 variables to predict postoperative ELP. When these formulas are applied to patients with normal eyes, the postoperative refractive results are accurate, but they tend to produce hyperopic surprise for highly myopic eyes. In recent years, several new formulas have emerged, including the Kane, EVO 2.0, and Hill–RBF formulas; many studies have confirmed the accuracies of these new formulas for highly myopic eyes. To our knowledge, most studies and subgroup comparisons have considered only the distributions of the AL data. However, other eye parameters (eg, ACD, LT, and keratometry) may also cause considerable bias. Gökce et al found that, for eyes with normal AL, changes in ACD led to significant differences in IOL formula accuracy. Hipólito-Fernandes et al divided patients with normal AL into 9 groups according to ACD and LT; they found that a thicker lens was associated with greater hyperopic surprise. For patients with high myopia, only 1 study, by Yang et al, reported the effect of ACD on the third-generation formulas (SRK/T, Holladay I, and Hoffer Q ) and fourth-generation formula (Haigis ).

This study was performed to investigate the effects of ACD on the accuracies of 6 IOL calculation formulas (Kane, EVO 2.0, Barrett Universal II, Olsen, SRK/T, and Haigis ) in cataract patients with elongated AL (≥26 mm).



This retrospective case series study included 106 eyes of 106 patients who had been diagnosed with high myopia and treated with cataract surgery, combined with IOL implantation, in the cataract department of the Eye Hospital of Wenzhou Medical University from March 2017 to September 2020. All surgeries were performed by the same experienced cataract surgeon (J.L.). The inclusion criteria were as follows: age ≥18 years, AL ≥26 mm, corrected distance visual acuity better than 20/40 within 3 months postoperatively, no intraoperative or postoperative complications, and follow-up within 1 to 3 months postoperatively. Patients were excluded if they had other ocular organic lesions (eg, strabismus, keratopathy, uveitis, glaucoma, and zonular fiber relaxation) and/or severe fundus lesions (eg, retinal detachment, choroidal neovascularization, and maculopathy). All included patients provided written informed consent for surgery and inclusion in research. This study was approved by the Institutional Review Board of the Eye Hospital of Wenzhou Medical University (ID: 2021-021-K-18-01) and conformed to the tenets of the Declaration of Helsinki.


According to the ACD measurements (including corneal thickness, ACD = AD + central corneal thickness) determined by Lenstar LS900 (Haag-Streit AG), patients were divided into 3 groups: shallow (ACD ≤ 3.00 mm), medium (3.00 mm < ACD < 3.5 mm), and deep (ACD ≥ 3.5 mm). The medium and deep groups were further divided into 4 subgroups according to an AL threshold of 28 mm: 1A (3.00 mm < ACD < 3.5 mm; 26 mm < AL < 28 mm), 1B (3.00 mm < ACD < 3.5 mm; AL ≥ 28 mm); 2A (ACD ≥ 3.5 mm; 26 mm < AL < 28 mm); and 2B (ACD ≥ 3.5 mm; AL ≥ 28 mm).


All eyes were measured with both the IOLMaster 500 (Carl Zeiss Meditech) and Lenstar LS900 to ensure the accuracy and reliability of preoperative biological parameters. Only the set of parameters from the Lenstar LS900 was used for refractive prediction error calculations, including AL, ACD, LT, keratometry, central corneal thickness (CCT), and white to white (WTW). All examinations were performed by professional operators. Patients underwent follow-up examinations at least 1 month postoperatively. Subjective refraction was assessed and the equivalent spherical equivalent (SE) values of the patients were calculated. Using the built-in software, IOL powers were calculated using the Haigis, SRK/T, Barrett Universal II (BU II), and Olsen formulas. The Kane and EVO 2.0 calculations were performed by using their respective public online calculation websites. The IOL constants for each formula was chosen using the method listed by the User Group for Laser Interference Biometry (ULIB).


SPSS Statistics software (version 25.0, IBM Corp) was used for statistical analysis. In accordance with the methods used by Wang et al and Hoffer et al, , the prediction error (PE) of each formula was calculated as the difference between actual postoperative SE and predicted SE. Negative PE indicated myopic shift, whereas positive PE indicated hyperopic shift. In addition, the absolute prediction error (AE) of each formula is calculated as the absolute value of PE. The mean prediction error (ME), mean absolute prediction error (MAE), median absolute prediction error (MedAE), and proportions of eyes within ±0.25 D, ±0.50 D, ±0.75 D, and ±1.00 D were calculated. In accordance with the statistical methods used by Hoffer et al and Aristodemou et al, , a single-sample t test or Wilcoxon signed-rank test was used to determine whether the MEs of each formula differed from zero; ME differences between formulas were tested by 1-way analysis of variance. The Friedman test was used to evaluate AE differences between formulas. Statistically significant differences were subjected to post hoc analysis using the Wilcoxon signed-rank test with Bonferroni correction. The Cochran Q test was used to compare the proportions of eyes within ±0.25 D, ±0.50 D, and ±1.00 D in each subgroup. The AE of each formula was compared between subgroups (medium ACD group vs. deep ACD group) using the Mann-Whitney U test; the proportions of eyes within ±0.25 D, ±0.50 D, and ±1.00 D were compared by the χ 2 test. Differences were considered statistically significant when P < 0.05.



In total, 106 eyes of 106 patients were included in this study: 46 men (43.4%) and 60 women (56.6%), involving 58 right eyes (54.7%) and 48 left eyes (45.3%). The mean age was 60.72 ± 12.04 years (range, 33-83 years). The implanted IOL types were the SN6CWS (Alcon, n = 23), SN6AT (Alcon, n = 29), 509M (Zeiss, n = 54). Table 1 shows the detailed ocular biological parameters among patients in this study.


Patient Biometric Characteristics (n = 106)

Parameter Mean ± SD/ Median (IQR) a Minimum Maximum
Axial length, mm 28.87 ± 1.88 26.14 33.61
Aqueous depth, mm 2.92 ± 0.36 2.09 3.71
Anterior chamber depth, mm b 3.46 ± 0.36 2.67 4.28
Mean of keratometry, D 44.38 ± 1.66 40.70 48.34
Lens thickness, mm 4.27 ± 0.40 2.58 5.47
Corneal central thickness, μm 539.49 ± 32.08 472 619
White-To-white, mm 11.67 ± 0.39 10.73 12.43
IOL power, D 10.0 (5.0) 1.0 18.0

IOL = intraocular lens, IQR = interquartile range.

a Data with a normal distribution are shown as the mean ± standard deviation, whereas data with a non-normal distribution are shown as the median and interquartile range.

b Anterior chamber depth was measured from corneal epithelium to lens)


In all patients, the MEs of the Kane and BUII formulas were −0.03 D and 0.08 D, respectively; these did not significantly differ from zero ( P = 0.548 and P = 0.126, respectively). The ME of the Haigis formula was highest and significantly differed from all other formulas ( P < 0.001). In addition, there was a significant pairwise difference between the Olsen and BUII formulas ( P < 0.001). The Haigis formula had a significantly higher MedAE compared with all other formulas ( P < 0.05); the Kane and EVO 2.0 formulas had significantly lower MedAEs compared with SRK/T ( P < 0.01). Concerning the proportions of eyes within ±0.25 D, significant differences were observed between the Kane and Haigis formulas ( P < 0.001), Kane and SRK/T formulas ( P = 0.002), and EVO 2.0 and Haigis formulas ( P = 0.013). Regarding the ±0.50 D, ±0.75 D, and ±1.00 D threshold, the Haigis formula proportion was significantly different from all other formulas ( P < 0.005, P < 0.001, P < 0.005, respectively), with the exception of SRK/T in ±0.75 D and ±1.00 D threshold ( P = 0.192, P = 0.694, respectively). Furthermore, the Olsen formula proportion was significantly higher than SRK/T in ±1.00 D threshold ( P = 0.026). Table 2 summarizes the MEs, MAEs, and MedAEs of the 6 IOL formulas, as well as the proportions of eyes that met the refractive thresholds for each formula. Figure 1 shows the violin distribution of PEs and AEs. Figure 2 , A shows the superimposed bar chart of the proportions of the 6 IOL formulas.


Predictive Outcomes of Each Formula in All Patients

Prediction Errors (D) Kane EVO 2.0 Olsen BU II SRK/T Haigis
ME ± SD −0.03 ± 0.50 a 0.16 ± 0.50 0.23 ± 0.48 0.08 ± 0.57 a 0.26 ± 0.65 0.63 ± 0.51
MAE ± SD 0.38 ± 0.32 0.40 ± 0.34 0.44 ± 0.30 0.45 ± 0.35 0.54 ± 0.43 0.67 ± 0.45
MedAE b 0.28 0.34 0.40 0.40 0.46 0.63
Percentage c (%)
±0.25 D d 47.17 40.57 34.91 33.96 26.42 21.70
±0.50 D d 70.75 67.92 64.15 59.44 54.72 34.91
±0.75 D d 85.85 84.91 84.91 83.02 74.53 63.21
±1.00 D d 92.45 95.28 97.17 92.45 86.79 81.13

BUII = Barrett Universal II, EVO = Emmetropia Verifying Optical, MAE = mean absolute error, ME = mean prediction error, MedAE = median absolute error.

a Single sample t test, P > 0.05.

b Friedman test, P < 0.001.

c Percentage of eyes with predictive error between ±0.25 D, ±0.50 D, ±0.75 D, and ±1.00 D.

d Cochrane Q test, P < 0.001.


Violin distributions of the prediction errors (A) and absolute prediction errors (B) of 6 intraocular lens formulas. The middle red lines represent the mean values, whereas the upper and lower red lines represent the quartile boundaries. EVO = Emmetropia Verifying Optical; BU II = Barrett Universal II.

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Jan 3, 2022 | Posted by in OPHTHALMOLOGY | Comments Off on Clinical Accuracy of 6 Intraocular Lens Power Calculation Formulas in Elongated Eyes, According to Anterior Chamber Depth

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