Introduction: This study aimed to determine the interchangeability of bilateral anterior chamber depth (ACD) in intraocular lens (IOL) power calculations for cataractous eyes and refractive outcomes using the unaffected fellow eye’s ACD in subluxated crystalline lenses. Methods: The predicted postoperative spherical equivalent (SE) calculated using the Kane formula with and without fellow eye’s ACD in 202 cataract patients was compared. Refractive outcomes of the newer formulas (the Kane, Barrett Universal II [BUII], and Pearl-DGS formulas) with affected eye’s ACD and with unaffected fellow eye’s ACD were compared in 33 eyes with lens subluxation (the affected eye) undergoing in-the-bag IOL implantation. The SD of the prediction error (PE) was assessed using the heteroscedastic method. Results: In 202 paired cataractous eyes, no marked ACD difference was found bilaterally; the predicted SE obtained without the fellow eye’s ACD was comparable with that calculated with the fellow eye one (p = 0.90), with a mean absolute difference of 0.03 ± 0.03 D. With the affected eye AL, keratometry, and ACD, the median absolute error (MedAE) was 0.38–0.64 D, and the percentage of PE within ±0.50 D was 30.30–57.58%. The unaffected eye’s ACD improved the results (MedAE, 0.35–0.49 D; the percentage of PE within ±0.50 D, 54.55–63.64%). The SDs of the BUII (0.82 D) and Pearl-DGS formulas (0.87 D) with the affected eye’s ACD were significantly larger than those of the Kane and Pearl-DGS formulas (both 0.69 D) with the unaffected eye’s ACD. Conclusion: Bilateral ACD was interchangeable in IOL power calculation for cataractous eyes when using the Kane formula. Unaffected eye’s ACD in lieu of affected eye’s ACD can enhance the accuracy of newer formulas in patients with unilateral subluxated lenses undergoing in-the-bag IOL implantation.

Although various surgical techniques exist for managing lens subluxation, achieving in-the-bag intraocular lens (IOL) placement remains the primary goal in this condition [1‒3]. However, even intracapsular IOL implantation can result in unsatisfactory postoperative refractive outcomes for such difficult eyes, especially when using newer formulas that incorporate anterior chamber depth (ACD) as a critical variable to calculate IOL power [4]. While these formulas have outperformed traditional third-generation formulas in routine cataract surgery, their accuracy is notably diminished in eyes with subluxated lenses, and in some studies, they were less accurate than third-generation formulas [4‒10]. Once the crystalline lens leaves its normal physiological position, even when the IOL is placed within the capsular bag, postoperative effective lens position (ELP) estimation using newer formulas can be erroneous because of the preoperatively unstable ACD caused by the dislocated lens.

Therefore, in such a situation, obtaining a more reliable ACD is presumably the approach to improving the performance of newer formulas. As the two eyes are naturally symmetrical, Olsen reported that the postoperative refractive status of the first operated eye could be used to refine the refractive outcome of the second operated eye [11]. Several studies have confirmed the comparability of biometric parameters between the right and left eyes, including ACD [11‒13]. Accordingly, we hypothesized that using the ACD of the unaffected eye could enhance the accuracy of newer formulas in cases of lens subluxation undergoing intracapsular IOL implantation.

The present study first assessed the interchangeability of bilateral ACD in IOL power calculation for cataractous eyes. This is because the use of the contralateral ACD measurement is a common practice when that of the surgical eye is unreliable or unmeasurable, but until now, it has never been substantiated by evidence. This step is a crucial prerequisite for adopting the unaffected eye’s ACD value as an approximation of unstable ACD in eyes with subluxated lenses. In addition, the present study had 2 objectives related to patients with unilateral lens subluxation undergoing in-the-bag IOL implantation: (1) to assess differences in preoperative biometric parameters (axial length [AL], keratometry [K], ACD, central corneal thickness, white-to-white, and lens thickness [LT]) between the two eyes and (2) to investigate whether using the unaffected eye’s ACD could enhance the newer formulas’ accuracy.

The study followed the principles of the Declaration of Helsinki and was approved by Shanghai East Hospital, School of Medicine, Tongji University, Shanghai, China.

Cataractous Eyes

Age-related cataract surgery candidates without congenital diseases who visited our department between September 2022 and November 2022 were reviewed. The exclusion criteria included invalid biometry measurements, history of intraocular surgery, ocular trauma, uveitis, and glaucoma. AL, K, and ACD were measured using the IOLMaster 700 (Carl Zeiss Meditec AG, Jena, Germany). We categorized the included paired cataractous eyes based on the interocular AL differences as follows: differences ≥0.3 mm (group A), ≥0.3 and <0.6 mm (group B), ≥0.6 and <1.0 mm (group C), and ≥1.0 mm (group D). Interocular differences in AL, K, and ACD were assessed in the total sample and in the four groups, respectively.

To determine the interchangeability of the bilateral ACD in IOL power calculation, we conceptualized and implemented an extrapolation-based approach. The steps of this approach are described below. Calculations were performed using the same IOL model (SN60WF, Alcon Laboratories, Inc.). The constant (119.0) was adopted from the User Group for Laser Interference Biometry (ULIB) website. The Kane formula was used for the calculations. The right-eye AL, K, and ACD were first input to calculate the spherical equivalent (SE), and the IOL power corresponding to the minimum myopic SE was recorded. The SE of the recorded IOL power was recalculated by substituting the right-eye ACD with that of the left eye. In Groups A to D, we applied the same method to assess the predicted postoperative SE with and without fellow eye’s ACD in eyes with a longer AL (longer eye). The calculations were also repeated for eyes with a shorter AL (shorter eye), with and without fellow eye’s ACD. The difference in SE was defined as the postoperative SE predicted without the fellow eye’s ACD minus that predicted with the fellow eye’s ACD. The mean absolute differences were calculated.

Eyes with Subluxated Lenses

Patients diagnosed with subluxated lenses who were treated surgically between October 2020 and July 2023 were reviewed. The inclusion criteria were patients with unilateral subluxated lenses (the affected eye), aged >18 years, who underwent in-the-bag IOL implantation using a capsular tension ring and intrascleral fixation of the implantable capsular hook as we previously described [14]. The surgery was performed by one of the authors (H.J.) with manifest refraction conducted at least 1 month postoperatively. The models and powers of the implanted IOLs were reviewed from electronic medical records. The exclusion criteria were invalid biometry for both eyes and the unaffected eye with corneal diseases, pseudophakia, phacodonesis, uveitis, glaucoma, trauma, or a surgical history. Patients with congenital diseases that can cause bilateral ACD abnormalities, including Marfan syndrome, homocystinuria, Weill-Marchesani syndrome, and aniridia, were excluded.

Preoperatively, biometry examination of the two eyes was performed using the IOLMaster 700, including measurements of AL, K, ACD, central corneal thickness, white-to-white, and LT. The ULIB website was consulted to determine IOL constants according to the implanted IOL model. Six formulas were analyzed in the present study. The IOL formulas and corresponding websites are as follows:

We grouped the formulas based on the input parameters used: group 1 used only the affected eye’s AL, K, and ACD in the three newer formulas (the Kane, BUII, and Pearl-DGS formulas); group 2 used the affected eye’s AL and K and the unaffected eye’s ACD in the three newer formulas. Third-generation formulas (the SRK/T, Holladay 1, and Hoffer Q formulas) predict IOL power more accurately than newer ones in cases of lens subluxation [4, 5]. Therefore, the accuracy of the third-generation formulas was analyzed (group 3rd generation) and compared with the above two groups. Notably, all three formulas in group 3rd generation do not use the ACD as a parameter in the calculation.

The prediction error (PE) was calculated as the actual postoperative SE minus the predicted SE, according to the implanted IOL power. A negative PE indicates a myopic error, whereas a positive PE indicates a hyperopic error. The mean absolute error (MAE), median absolute error (MedAE), and percentage of eyes with PE within ±0.50, ±1.00, and ±2.00 diopters (D) were calculated.

Statistical Analysis

Statistical analyses were performed using Prism (GraphPad Software, USA), R software (version 4.3.0), and Microsoft Excel (Microsoft Corp., USA). Based on the normality determined by the Kolmogorov-Smirnov test, the interocular differences in biometry and predicted postoperative SEs were compared using a paired samples t test or Wilcoxon signed-rank test. Pearson or Spearman correlation coefficients of parameters were calculated between the 2 eyes of cataractous patients based on the distribution type of parameters. The SD of PEs served as the primary measure to compare refractive outcomes between the formulas in cases of subluxated lenses using the heteroscedastic method described by Holladay et al. [15]. The p value was adjusted for multiple comparisons, and statistical significance was defined as p < 0.05.

The interchangeability of bilateral ACD in IOL power calculation was assessed in 202 paired cataractous eyes of 202 patients. The performance of IOL formulas after substituting the affected eye’s ACD with the unaffected eye’s ACD in cases of lens subluxation was evaluated in 33 paired eyes of 33 patients.

IOL Power Calculation in Cataractous Eyes

The mean age of the cataractous patients (n = 202) was 70.16 ± 8.20 years (range: 60–89 years); there were 102 women (50.50%). The AL of the right eye was 24.55 ± 2.18 mm, and the ACD was 3.02 ± 0.49 mm, both of which did not show marked differences compared to the left eye (AL = 24.48 ± 2.07 mm, p = 0.24; ACD = 3.03 ± 0.46 mm, p = 0.57; Table 1). Sixty-three patients (32.67%) had an interocular AL difference of ≥0.3 mm. Among the 63 patients in group A, the longer eye ACD was significantly deeper than that of the fellow eye (p = 0.01).

Table 1.

AL and ACD between the two eyes of cataract patients

AL, mmp valueCorrelation coefficientp valueACD, mmp valueCorrelation coefficientp value
Total (n = 202) 
 Right eye 24.55±2.18 0.24 0.9128 <0.001* 3.02±0.49 0.57 0.9038 <0.001* 
 Left eye 24.48±2.07 3.03±0.46 
Group Aa (n = 63) 
 Longer eye 26.42±2.46 <0.001* 0.8359 <0.001* 3.20±0.47 0.01* 0.9085 <0.001* 
 Shorter eye 25.25±2.26 3.14±0.48 
Group Bb (n = 27) 
 Longer eye 25.26±1.53 <0.001* 0.9983 <0.001* 3.17±0.45 0.21 0.8535 <0.001* 
 Shorter eye 24.84±1.52 3.11±0.43 
Group Cc (n = 14) 
 Longer eye 27.06±2.55 <0.001* 0.9989 <0.001* 3.32±0.36 0.12 0.9172 <0.001* 
 Shorter eye 26.25±2.52 3.25±0.35 
Group Dd (n = 22) 
 Longer eye 27.44±2.81 <0.001* 0.7845 <0.001* 3.17±0.57 0.10 0.9438 <0.001* 
 Shorter eye 25.12±2.71 3.10±0.59 
AL, mmp valueCorrelation coefficientp valueACD, mmp valueCorrelation coefficientp value
Total (n = 202) 
 Right eye 24.55±2.18 0.24 0.9128 <0.001* 3.02±0.49 0.57 0.9038 <0.001* 
 Left eye 24.48±2.07 3.03±0.46 
Group Aa (n = 63) 
 Longer eye 26.42±2.46 <0.001* 0.8359 <0.001* 3.20±0.47 0.01* 0.9085 <0.001* 
 Shorter eye 25.25±2.26 3.14±0.48 
Group Bb (n = 27) 
 Longer eye 25.26±1.53 <0.001* 0.9983 <0.001* 3.17±0.45 0.21 0.8535 <0.001* 
 Shorter eye 24.84±1.52 3.11±0.43 
Group Cc (n = 14) 
 Longer eye 27.06±2.55 <0.001* 0.9989 <0.001* 3.32±0.36 0.12 0.9172 <0.001* 
 Shorter eye 26.25±2.52 3.25±0.35 
Group Dd (n = 22) 
 Longer eye 27.44±2.81 <0.001* 0.7845 <0.001* 3.17±0.57 0.10 0.9438 <0.001* 
 Shorter eye 25.12±2.71 3.10±0.59 

ACD, anterior chamber depth.

aGroup A: interocular AL difference ≥0.3 mm.

bGroup B: interocular AL difference ≥0.3 and <0.6 mm.

cGroup C: interocular AL difference ≥0.6 and <1.0 mm.

dGroup D: interocular AL difference ≥1.0 mm.

*Significant difference (p < 0.05).

We observed in the overall cataract sample that for the right eye, the predicted postoperative SE obtained using the right-eye ACD was not statistically different from that calculated using the left-eye ACD, with a mean absolute difference value of 0.03 ± 0.03 D and a high correlation coefficient (Table 2). The predicted postoperative SE with and without the fellow eye’s ACD was highly correlated within the four groups (groups A to D), with a correlation coefficient ranging from 0.8738 to 0.9745. An in-depth investigation into these four groups revealed that adopting fellow eye’s ACD as a substitute resulted in a significantly different predicted SE compared to the outcome without fellow eye’s ACD; however, the mean absolute difference ranged from 0.02 to 0.04 D. These results suggest that the predicted SEs with and without fellow eye’s ACD are comparable in the clinical setting.

Table 2.

Predicted SE obtained using different combinations of AL and ACD

Predicted SE, diopterp valueCorrelation coefficientp valueMean difference, diopterMean absolute difference, diopter
Total (n = 202) 
 Right eye’s AL + K + ACD −0.16±0.10 0.90 0.9255 <0.001* 0.00±0.05 0.03±0.03 
 Right eye’s AL + K + left eye’s ACD −0.16±0.11 
Group Aa (n = 63) 
 Longer eye’s AL + K + ACD −0.15±0.10 <0.001* 0.9189 <0.001* 0.02±0.04 0.03±0.03 
 Longer eye’s AL + K + shorter eye’s ACD −0.16±0.10 
 Shorter eye’s AL + K+ ACD −0.15±0.09 <0.001* 0.9104 <0.001* −0.02±0.04 0.03±0.03 
 Shorter eye’s AL + K + longer eye’s ACD −0.13±0.09 
Group Bb (n = 27) 
 Longer eye’s AL + K + ACD −0.14±0.10 0.03* 0.8807 <0.001* 0.02±0.05 0.04±0.04 
 Longer eye’s AL + K + shorter eye’s ACD −0.16±0.10 
 Shorter eye’s AL + K + ACD −0.18±0.09 0.03* 0.8738 <0.001* −0.02±0.04 0.03±0.04 
 Shorter eye’s AL + K + longer eye’s ACD −0.16±0.09 
Group Cc (n = 14) 
 Longer eye’s AL + K + ACD −0.13±0.09 0.02* 0.9517 <0.001* 0.02±0.03 0.03±0.03 
 Longer eye’s AL + K + shorter eye’s ACD −0.15±0.10 
 Shorter eye’s AL + K + ACD −0.14±0.11 0.02* 0.9745 <0.001* −0.02±0.03 0.02±0.02 
 Shorter eye’s AL + K + longer eye’s ACD −0.12±0.11 
Group Dd (n = 22) 
 Longer eye’s AL + K + ACD −0.17±0.10 0.03* 0.9694 <0.001* 0.01±0.03 0.02±0.02 
 Longer eye’s AL + K + shorter eye’s ACD −0.18±0.10 
 Shorter eye’s AL + K + ACD −0.12±0.08 0.10 0.8776 <0.001* −0.02±0.04 0.03±0.04 
 Shorter eye’s AL + K + longer eye’s ACD −0.11±0.09 
Predicted SE, diopterp valueCorrelation coefficientp valueMean difference, diopterMean absolute difference, diopter
Total (n = 202) 
 Right eye’s AL + K + ACD −0.16±0.10 0.90 0.9255 <0.001* 0.00±0.05 0.03±0.03 
 Right eye’s AL + K + left eye’s ACD −0.16±0.11 
Group Aa (n = 63) 
 Longer eye’s AL + K + ACD −0.15±0.10 <0.001* 0.9189 <0.001* 0.02±0.04 0.03±0.03 
 Longer eye’s AL + K + shorter eye’s ACD −0.16±0.10 
 Shorter eye’s AL + K+ ACD −0.15±0.09 <0.001* 0.9104 <0.001* −0.02±0.04 0.03±0.03 
 Shorter eye’s AL + K + longer eye’s ACD −0.13±0.09 
Group Bb (n = 27) 
 Longer eye’s AL + K + ACD −0.14±0.10 0.03* 0.8807 <0.001* 0.02±0.05 0.04±0.04 
 Longer eye’s AL + K + shorter eye’s ACD −0.16±0.10 
 Shorter eye’s AL + K + ACD −0.18±0.09 0.03* 0.8738 <0.001* −0.02±0.04 0.03±0.04 
 Shorter eye’s AL + K + longer eye’s ACD −0.16±0.09 
Group Cc (n = 14) 
 Longer eye’s AL + K + ACD −0.13±0.09 0.02* 0.9517 <0.001* 0.02±0.03 0.03±0.03 
 Longer eye’s AL + K + shorter eye’s ACD −0.15±0.10 
 Shorter eye’s AL + K + ACD −0.14±0.11 0.02* 0.9745 <0.001* −0.02±0.03 0.02±0.02 
 Shorter eye’s AL + K + longer eye’s ACD −0.12±0.11 
Group Dd (n = 22) 
 Longer eye’s AL + K + ACD −0.17±0.10 0.03* 0.9694 <0.001* 0.01±0.03 0.02±0.02 
 Longer eye’s AL + K + shorter eye’s ACD −0.18±0.10 
 Shorter eye’s AL + K + ACD −0.12±0.08 0.10 0.8776 <0.001* −0.02±0.04 0.03±0.04 
 Shorter eye’s AL + K + longer eye’s ACD −0.11±0.09 

ACD, anterior chamber depth; AL, axial length; K, keratometry; SE, spherical equivalent.

aGroup A: interocular AL difference ≥0.3 mm.

bGroup B: interocular AL difference ≥0.3 and <0.6 mm.

cGroup C: interocular AL difference ≥0.6 and <1.0 mm.

dGroup D: interocular AL difference ≥1.0 mm.

*Significant difference (p < 0.05).

IOL Power Calculation in Subluxated Lenses

The mean age of the patients (n = 33) with subluxated lenses was 59.27 ± 13.72 years (range: 25–85 years); there were 28 men (84.85%). The most common etiology was ocular trauma (n = 22, 66.67%). The detailed demographic information is presented in Table 3. As shown in Table 4, the ACD of the affected eye (2.76 ± 0.85 mm) was shallower than that of the unaffected eye (3.16 ± 0.40 mm, p = 0.01). The other ocular biometric parameters were comparable bilaterally, except for the LT (p < 0.001).

Table 3.

Demographic information of cases of subluxated lenses

ParametersValues
Age, years 59.27±13.72 
Male/female, n 28/5 
Right/left eye, n 17/16 
Etiologies, n 
 Ocular trauma 22 
 Unknown cause 
 Acute angle-closure glaucoma 
 Iatrogenic 
 High myopia 
 Brunescent cataract 
Implanted IOL models, n 
 SN60WF 11 
 ZA9003 
 PY-60AD 
 ZCB00 
 Akreos Adapt AO 
 PC525 
ParametersValues
Age, years 59.27±13.72 
Male/female, n 28/5 
Right/left eye, n 17/16 
Etiologies, n 
 Ocular trauma 22 
 Unknown cause 
 Acute angle-closure glaucoma 
 Iatrogenic 
 High myopia 
 Brunescent cataract 
Implanted IOL models, n 
 SN60WF 11 
 ZA9003 
 PY-60AD 
 ZCB00 
 Akreos Adapt AO 
 PC525 

IOL, intraocular lens.

SN60WF (Alcon Laboratories, TX, USA); ZA9003 (Abbott Medical Optics, CA, USA); PY-60AD (Hoya Surgical Optics, Tokyo, Japan.); ZCB00 (Abbott Medical Optics, CA, USA); Akreos Adapt AO (Bausch & Lomb, NY, USA); PC525 (Ophtec, Groningen, Netherlands).

Table 4.

Comparison of biometric measurements between the affected eye and the unaffected eye

BiometryThe affected eyeThe unaffected eyep value
AL, mm 24.34±2.11 24.19±1.70 0.43 
Average K, D 43.65±1.11 43.60±1.23 0.57 
ACD, mm 2.76±0.85 3.16±0.40 0.01* 
CCT, μm 544.70±37.92 538.20±29.06 0.09 
WTW, mm 11.93±0.71 11.83±0.42 0.84 
LT, mm 3.76±1.02 4.63±0.43 <0.001* 
BiometryThe affected eyeThe unaffected eyep value
AL, mm 24.34±2.11 24.19±1.70 0.43 
Average K, D 43.65±1.11 43.60±1.23 0.57 
ACD, mm 2.76±0.85 3.16±0.40 0.01* 
CCT, μm 544.70±37.92 538.20±29.06 0.09 
WTW, mm 11.93±0.71 11.83±0.42 0.84 
LT, mm 3.76±1.02 4.63±0.43 <0.001* 

ACD, anterior chamber depth; AL, axial length; CCT, central corneal thickness; D, diopter; K, keratometry; LT, lens thickness; WTW, white-to-white.

*Significant difference (p < 0.05).

Table 5 presents the performance of the formulas in the three groups (group 3rd generation, group 1, and 2). The SDs of the third-generation formulas were ranked in ascending order as follows: SRK/T (0.74 D), Holladay 1 (0.76 D), and Hoffer Q (0.77 D). The lowest to highest SD values were 0.75 D (Kane) to 0.87 D (Pearl-DGS) in group 1, and 0.69 D (Kane and Pearl-DGS) to 0.70 D (BUII) in group 2. The heteroscedastic analysis indicated that the SD of the BUII formula (0.82 D) in group 1 was significantly higher than that of the Kane and Pearl-DGS formulas (both 0.69 D) in group 2 (p < 0.001; online suppl. Table 1; for all online suppl. material, see https://doi.org/10.1159/000538234). The Pearl-DGS formula (0.87 D) in group 1 had a significantly higher SD than the Kane (0.69 D), BUII (0.70 D), and Pearl-DGS (0.69 D) formulas in group 2.

Table 5.

Predictive outcomes of IOL formulas

FormulasPE±SD, DMedAE, DMAE, D±0.5 D, %±1.0 D, %±2.0 D, %
Group 3rd generationa 
 SRK/T −0.11±0.74 0.37 0.54 60.61 84.85 96.97 
 Holladay 1 −0.06±0.76 0.32 0.56 57.58 87.88 100.00 
 Hoffer Q −0.04±0.77 0.56 0.60 45.45 81.82 100.00 
Group 1b 
 Kane −0.17±0.75 0.38 0.58 57.58 84.85 96.97 
 BUII 0.01±0.82 0.60 0.65 39.39 87.88 96.97 
 Pearl-DGS 0.05±0.87 0.64 0.71 30.30 72.73 90.91 
Group 2c 
 Kane −0.21±0.69 0.35 0.52 63.64 84.85 100.00 
 BUII −0.10±0.70 0.46 0.52 57.58 87.88 100.00 
 Pearl-DGS −0.12±0.69 0.49 0.52 54.55 90.91 96.97 
FormulasPE±SD, DMedAE, DMAE, D±0.5 D, %±1.0 D, %±2.0 D, %
Group 3rd generationa 
 SRK/T −0.11±0.74 0.37 0.54 60.61 84.85 96.97 
 Holladay 1 −0.06±0.76 0.32 0.56 57.58 87.88 100.00 
 Hoffer Q −0.04±0.77 0.56 0.60 45.45 81.82 100.00 
Group 1b 
 Kane −0.17±0.75 0.38 0.58 57.58 84.85 96.97 
 BUII 0.01±0.82 0.60 0.65 39.39 87.88 96.97 
 Pearl-DGS 0.05±0.87 0.64 0.71 30.30 72.73 90.91 
Group 2c 
 Kane −0.21±0.69 0.35 0.52 63.64 84.85 100.00 
 BUII −0.10±0.70 0.46 0.52 57.58 87.88 100.00 
 Pearl-DGS −0.12±0.69 0.49 0.52 54.55 90.91 96.97 

BUII, Barrett Universal II; D, diopter; IOL, intraocular lens; MAE, mean absolute error; MedAE, median absolute error; PE, prediction error.

aGroup 3rd generation: using the affected eye’s axial length and keratometry.

bGroup 1: using the affected eye’s axial length, keratometry, and anterior chamber depth.

cGroup 2: using the affected eye’s axial length and keratometry and the unaffected eye’s anterior chamber depth.

Figure 1 displays the distribution of eyes within different PE ranges and MAEs for the various formulas. The Kane formula in group 2 had the highest percentage of eyes within ±0.50 D (63.64%), followed by the SRK/T (60.61%). Substituting the affected eye’s ACD with the unaffected eye’s ACD improved the percentage range of the PEs within ±0.50 D from 30.30 to 57.58% in group 1 to 54.55–63.64% in group 2; meanwhile, the MedAE range decreased from 0.38–0.64 D in group 1 to 0.35–0.49 D in group 2. The accuracy of the newer formulas with the unaffected eye’s ACD regarding obtaining PEs within ±0.50 and ±1.00 D was comparable to the SRK/T and Holladay 1 formulas.

Fig. 1.

a Stacked histograms comparing the percentage of eyes within certain PE ranges for the intraocular lens (IOL) power calculation formulas. b Box plot graphs presenting the absolute PEs of the IOL power calculation formulas. BUII = Barrett Universal II. Group 1 used only the affected eye’s axial length (AL), keratometry (k), and anterior chamber depth (ACD); group 2 used the affected eye’s AL and K and the unaffected eye’s ACD in the three newer formulas.

Fig. 1.

a Stacked histograms comparing the percentage of eyes within certain PE ranges for the intraocular lens (IOL) power calculation formulas. b Box plot graphs presenting the absolute PEs of the IOL power calculation formulas. BUII = Barrett Universal II. Group 1 used only the affected eye’s axial length (AL), keratometry (k), and anterior chamber depth (ACD); group 2 used the affected eye’s AL and K and the unaffected eye’s ACD in the three newer formulas.

Close modal

One of the central goals of refractive cataract surgery is to achieve the desired postoperative refractive state [9, 16]. Misestimation of postoperative ELP is a major source of error in IOL power calculations [9, 17]. Traditional third-generation formulas, such as SRK/T, Holladay 1, and Hoffer Q, only use preoperative AL and K for postoperative ELP estimation. Newer formulas, including Kane, BUII, and Pearl-DGS, add ACD to IOL power calculation. Previous studies have shown that newer formulas outperform third-generation formulas in routine cataract surgery [6‒9]. However, in cases of lens subluxation, formulas integrating ACD to predict refractive outcomes might result in poorer performance than traditional ones. Lian et al. [5] found that the accuracy of the SRK/T formula in patients with congenital ectopia lentis was better than that of newer formulas when performing transscleral fixation of the IOL. Existing formulas were derived assuming intracapsular IOL implantation; therefore, IOL fixation outside the capsular bag would inherently lead to IOL power calculation errors. An essential premise of the present study was the achievement of in-the-bag IOL implantation. However, even with intracapsular IOL implantation, newer formulas might still lead to considerable misprediction of IOL power in eyes with subluxated lenses. Zhang et al. [4] reported that the accuracy of the traditional formulas was higher than that of the BUII formula in patients with lens subluxation secondary to Marfan syndrome who underwent intracapsular IOL placement with modified capsular tension rings.

Abnormal ACD values obtained by the biometer are a crucial contributor to the decreased accuracy of newer formulas in cases of lens subluxation. When the lens is dislocated from its normal physiological position, it may be closer to the anterior chamber or vitreous body, resulting in inaccurate ACD measurements. Previous studies have shown that the MAE of the second operated eye can be refined by adjusting the IOL power calculation based on the postoperative results of the first operated eye [11, 18]. While this approach might be feasible in patients with bilateral lens subluxation undergoing sequential surgeries, it is impractical for those with unilateral lens subluxation, as phacoemulsification and IOL implantation are not typically performed sequentially in each eye. This was the case for most patients in the present study who had unilateral lens subluxation, primarily due to ocular trauma. Our hypothesis was that the unaffected eye’s ACD could serve as an approximation of the ACD of the affected eye prior to lens subluxation, given the bilateral symmetry. However, as far as our knowledge goes, the potential improvement in refractive outcomes for eyes with lens subluxation through the adoption of unaffected eye’s ACD has not been previously discussed.

Using the unaffected eye’s ACD to enhance the refractive prediction for lens subluxation requires the following two prerequisites to be met: First, the ACD values of both eyes should be highly comparable in the general population and should be so postoperatively. Second, the ACD values should be interchangeable bilaterally in IOL power calculation for routine cataract surgery. The first point was confirmed in previous studies [12, 13]. We investigated the second point in cataractous eyes. The present results demonstrated that the Kane formula with and without fellow eye’s ACD exhibited comparable results in predicting SEs in cataractous eyes. Moreover, as shown in Table 2, even within paired eyes with an interocular AL difference ≥1.0 mm, adopting the fellow eye’s ACD did not induce a clinically significant change in the predicted SE for the longer eye, which was also observed for the shorter eye.

The accuracy of the newer formulas with and without the unaffected eye’s ACD was assessed using the heteroscedastic statistical method [15]. Third-generation formulas were selected as the benchmark because previous studies confirmed their higher accuracy than newer ones in eyes with lens subluxation [4, 5]. Holladay et al. [15] proposed that SD is the most accurate parameter for evaluating the accuracy of IOL power calculation formulas. The SRK/T formula had the lowest SD (0.74 D) among the third-generation formulas, followed by the Holladay 1 (0.76 D) and Hoffer Q (0.77 D) formulas. The SD range of the newer formulas with the affected eye’s ACD (group 1) was 0.75–0.87 D, which was numerically higher than that of the third-generation ones, consistent with previous studies [4, 5]. Furthermore, the MedAEs between group 3rd generation and group 1 were also analyzed. As expected, the third-generation formulas also surpassed the newer ones in two crucial performance metrics: MedAE and the percentage of PEs within ±0.50 D. To illustrate, the MedAE of the third-generation formula ranged from 0.37 D to 0.56 D, whereas that of the newer formula with the affected eye’s ACD ranged from 0.38 D to 0.64 D. Group 2 was set to determine whether substituting the affected eye’s ACD value with a more reliable unaffected eye’s ACD value could improve the performance of the newer formulas. The SD range of the newer formulas with the unaffected eye’s ACD (group 2) decreased to 0.69–0.70 D. Moreover, the heteroscedastic method revealed that the SDs of the BUII and Pearl-DGS formulas with the affected eye’s ACD were significantly larger than several newer formulas with unaffected eye’s ACD (online suppl. Table 1). The present study reflected a real-world scenario, as the IOL constant was adopted from the ULIB, in line with routine clinical practice and a recent study [5, 19]. The above-mentioned results suggest that the performance of the newer formulas in the context of lens subluxation can be improved when the unaffected eye’s ACD is replaced by the affected eye’s ACD.

Interestingly, in contrast to the BUII and Pearl-DGS formulas, the Kane, even with the affected eye’s ACD, demonstrated a level of accuracy comparable to that of the third-generation formulas, consistent with a previous study [5]. Although the exact structure of the Kane formula remains undisclosed, we assumed that the weight of the ACD within the formula may be relatively modest. Alternatively, the Kane formula presumably employs a computational framework adept at mitigating the errors that may be introduced by atypical ACD values. Nevertheless, in cases of lens subluxation, substituting affected eye’s ACD with unaffected eye’s ACD is still advocated for the Kane formula. This recommendation was substantiated by the data presented in Table 5, which illustrates that the use of the unaffected eye’s ACD leads to a reduction in the SD of the Kane from 0.75 D to 0.69 D, along with a decrease in the MedAE from 0.38 D to 0.35 D.

Our study has two main limitations. First, the sample of lens subluxation cases was small; therefore, a large-sample study is required to verify our findings. Second, multiple IOL types with inherently different characteristics were used in this study.

In summary, the present study suggests that bilateral ACD can be used interchangeably in IOL power calculation for cataract patients when using the Kane formula. Additionally, the newer formulas that used unaffected fellow eye’s ACD in lieu of affected eye’s ACD can serve as a reliable option for IOL power calculations in patients with unilateral lens subluxation undergoing in-the-bag IOL implantation.

This study followed the Declaration of Helsinki and was approved by the Institutional Review Board of Shanghai East Hospital (approval No. 2022-221). The need for informed consent was waived for cataract surgery candidates by the Institutional Review Board of Shanghai East Hospital. All patients with subluxated lenses provided written informed consent before surgery.

The authors have no conflicts of interest to declare.

This study was supported by the fund for Shanghai Science and Technology Innovation (No. 20Y11910900).

W.L. contributed to the conceptualization and was involved in writing, reviewing, and editing. Z.C. and Y.H. contributed to methodology and data curation. H.J. contributed to the conceptualization, methodology, and review. All authors have read and approved the final manuscript.

All relevant data have been included in the article. Further inquiries can be directed to the corresponding author.

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