Evaluation of the crystalline lens diameter using swept-source optical coherence tomography

Abstract

Objective

To evaluate the estimated lens diameter (eLD) of the crystalline lens in a large European cohort.

Methods and analysis

Data sets from an Austrian population acquired between 2020 and 2022 were analysed in this study. Measurements included optical biometry (IOLMaster 700, Carl Zeiss Meditec AG, Germany) as well as anterior segment optical coherence tomography (CASIA2, Tomey, Japan). For eLD prediction, three different machine learning approaches were implemented.

Results

In total, 2352 eyes of 2352 patients were included in this study. The eLD was normally distributed with a mean value of 10.18±0.56 mm, showing a statistically significant difference (p=0.008) between females and males (10.16±0.54 mm and 10.22±0.57 mm, respectively). There was a low but significant correlation (p<0.01 for all) with age (r=0.246), lens thickness (r=0.265), white-to-white (r=0.122), corneal radii (r=0.090), axial eye length (r=0.092), anterior chamber depth (r=−0.060), decentration (r=−0.087) and tilt (r=−0.159), respectively. Subanalysis of short and long eyes yielded no significant difference in eLD. For eLD prediction, age and lens thickness appeared to be relevant parameters, with all three models demonstrating low predictive accuracy.

Conclusion

The crystalline lens diameter followed a normal distribution with no significant differences between short and long eyes. All three models demonstrated low predictive accuracies, suggesting that reliable prediction of eLD is currently not attainable.

WHAT IS ALREADY KNOWN ON THIS TOPIC

• Routine direct measurement of the crystalline lens diameter is not feasible within routine clinical care with the currently available technologies.

• Swept-source anterior segment optical coherence tomography can provide an estimation of the lens diameter based on extrapolation of the anterior and posterior curvature of the lens.

WHAT THIS STUDY ADDS

• In a large real-world cohort, the estimated lens diameter was normally distributed, showing weak correlations with standard biometric parameters and no significant difference between short and long eyes.

• Selected machine-learning approaches were unable to accurately predict the estimated lens diameter from the available biometric parameters.

HOW THIS STUDY MIGHT AFFECT RESEARCH, PRACTICE OR POLICY

• This study provides a large European reference cohort characterising the distribution of the estimated lens diameter, offering a benchmark for future investigations on the subject.

Introduction

The postoperative refractive outcome after cataract surgery is determined by several factors, with intraocular lens (IOL) positioning playing a crucial role. IOL power calculation formulae aim at predicting the effective lens position (ELP) with different parameters. Discrepancies between the estimated and ELP contribute significantly to postoperative refractive errors, as demonstrated in a study by Norrby.¹ Different concepts in IOL power calculation have been suggested to tackle this issue. However, to our knowledge, none of the commercially available concepts includes the lens diameter (LD) as a potentially influential parameter for ELP prediction in their calculations. The reason could be the lack of measurability of the peripheral part of the lens using optical biometry methods due to the iris.

Ultrasound biomicroscopy (UBM) or MRI have been used in several studies to obtain the LD, but in clinical routine, these measurements are often not available, not precise enough or too expensive and time-consuming for everyday use.^{2 3}

Therefore, LD has not played a major role in IOL calculation thus far, as the issue of accurate determination for potential downstream implantation remains.

The aim of this study was to evaluate the estimated LD (eLD) and its relation to the parameters obtained by optical biometry and swept-source optical coherence tomography (ss-OCT) imaging. Furthermore, different eLD prediction models using machine learning were compared with anterior segment OCT (AS-OCT) based estimations of the LD.

Methods

Study design

This retrospective study included patients who received both biometric and AS-OCT measurements between 2020 and 2022. Imaging was performed as part of routine clinical care for a range of indications, including predominantly preoperative cataract assessment, refractive consultation and disease monitoring. In all cases, data were taken from one clinic (Kepler University Clinic Linz, Austria) from two devices: optical biometry (IOLMaster 700, Carl Zeiss Meditec AG, Jena, Germany) and AS-OCT (CASIA2, Tomey, Japan). If one or both measurements were missing, the patient was excluded from analysis. Patients were not involved in setting the research question or outcome measures, as this was a retrospective analysis.

Inclusion and exclusion criteria

During examination, patients were measured using the two devices stated above. Scans with insufficient quality or insufficient lens segmentation were excluded. Eyes with cataract and corneal disease were retained to preserve the real-world character of the data. The dataset was filtered for multiple measurements as well as missing data. Only the right eye of every patient was included for analysis.

Measurements

Obtained data were anonymised before being exported to a comma-separated value table via the export function of both devices. Data tables were shortened to only the parameters needed for our data analysis, namely the following.

Optical biometry

Axial eye length in mm (AL), central lens thickness in mm (LT), anterior chamber depth in mm (ACD; distance from the corneal apex (epithelium) to the anterior lens apex), horizontal corneal diameter in mm (white to white (W2W)), front radius of the cornea in mm (Rmean; mean value of steep and flat curvature of the cornea), Chang-Waring chord (CW; position of the Purkinje reflex PI relative to the corneal centre) and central corneal thickness (CCT; distance from the anterior (epithelium) to the posterior (endothelium) surface of the cornea).

AS-OCT created 16 distinct two-dimensional images of every patient’s crystalline lens at different angles to obtain the morphology of the lens. The analysis included crystalline lens tilt, which was defined as the angle between the lens axis and the axis normal to the corneal vertex (horizontal and vertical) in degrees, decentration of the crystalline lens in mm (defined as the distance between reference axis and lens center), as well as the eLD, which was extrapolated semiautomatically using the anterior and posterior curvature of the lens and double-checked to ensure accurate segmentation.

Analysis

Analysis was performed using Microsoft Excel (V.16.12, Microsoft Corporation, USA) and SPSS software (SPSS V.29.0, IBM, USA) as well as Python (V.3.10) using Scikit-learn (V.1.8.0).

Descriptive analysis was performed, and results are presented as mean, SD and range. Data were inspected for implausible measurements as well as normal distribution, which was evaluated using histograms and Q-Q plots. A p-value below 0.05 was considered statistically significant.

For the prediction of the eLD, three models were evaluated, including a partial least squares (PLS) model, a random forest approach and a support vector regression (SVR) model. The same 11 predictors were used for all three approaches: AL, Rmean, ACD, LT, CCT, W2W, CW, decentration, tilt, age and gender. No data-driven feature selection was performed.

For all models, data were split into a training set (80%) and test set (20%) using a fixed random seed. The test set was not included in model development or hyperparameter selection.

Hyperparameters were tuned by grid search with fivefold cross-validation on the training set, minimising the mean root-mean-square error (RMSE). The hyperparameters identified were five components for the PLS, 300 trees, no maximum depth, √p features per split, and a minimum of 10 samples per leaf for the random forest and C=0.1, ε=0.4 and γ=0.1 for the SVR (radial basis function kernel). Final models were trained on the entire training dataset using optimised hyperparameters.

Performance was evaluated on the test data, which was strictly reserved for the final assessment, evaluating R², RMSE and mean absolute error (MAE). For assessment of contribution to the prediction, permutation importance was evaluated.

Results

In total, 2352 right eyes of 2352 patients were included for the analysis. 1270 females (54.0%) and 1082 males (46.0%) were included. Mean age was 70.7±10.8 years. A descriptive analysis of the biometric data is displayed in table 1.

Table 1. Descriptive analysis of the biometric data as provided by optical biometry.

	Mean	SD	Median	Min	Max
Axial eye length (mm)	23.58	1.41	23.37	19.12	36.26
Mean corneal radii (mm)	7.69	0.29	7.69	5.10	8.95
Anterior chamber depth (mm)	3.09	0.41	3.08	1.87	4.61
Lens thickness (mm)	4.63	0.43	4.64	3.24	5.91
Central corneal thickness (mm)	0.545	0.040	0.545	0.256	0.703
White to white (mm)	11.97	0.40	11.97	10.50	14.68
Chang-Waring chord (mm)	0.36	0.18	0.34	0.01	1.68

Overall, the eLD was normally distributed with a mean value of 10.18±0.56 mm (median: 10.24 mm, range: 6.84–11.77 mm), as displayed in figure 1a,b. One outlier with an eLD of 6.84 mm was found. For this outlier, analysis of a second available scan yielded similar results. Evaluation of the eLD in the fellow eye showed a rather normal eLD with a value of 10.64 mm. No other factors explaining the deviation were found.

Figure 1. (a) Estimated lens diameter follows a normal distribution. (b) Boxplot illustrating the distribution of the lens diameter. One outlier with a value of 6.84 mm was found.

For females, eLD was 10.16±0.54 mm, while for males, eLD was 10.22±0.57 mm. There was a minor but significant difference between genders (p=0.008) and a low correlation with age (r=0.246; p<0.001).

The eLD showed a low but significant correlation with LT (r=0.265; p<0.001) and W2W (r=0.122; p<0.001). There was also a significant but most likely not relevant correlation with Rmean (r=0.090; p<0.001), AL (r=0.092; p<0.001), ACD (r=−0.060; p=0.004), decentration (r=−0.087; p<0.001) and tilt (r=−0.159; p<0.001).

The data set included 166 short eyes with an AL <22.00 mm and 120 long eyes with an AL >26.00 mm, with a mean eLD of 10.08±0.53 mm and 10.18±0.50 mm, respectively. There was a mean difference of −0.10 mm (95% CI −0.22 to 0.02 mm; Welch’s t=−1.671, p=0.096; Cohen’s d=−0.199; figure 2a). Sensitivity power analysis indicated a smallest detectable effect of d=0.337, corresponding to a difference of 0.17 mm between groups. There was a negligible correlation between eLD and the ratio between ACD and AL (r=−0.093; p<0.001). The relation between eLD and ACD and eLD and ACD/AL is displayed in figure 2b,c, respectively.

Figure 2. (a) Distribution of the estimated lens diameter in relation to AL. Only a low correlation (r=0.092; p<0.001) was found. (b) Distribution of estimated lens diameter in relation to ACD. Pearson correlation showed negligible correlation (r=−0.060; p<0.01). (c) Distribution of estimated lens diameter in relation to ACD/AL. Pearson correlation showed a negligible correlation (r=−0.093; p<0.001). ACD, anterior chamber depth; AL, axial eye length.

In a second step, three different approaches were used to predict the eLD.

The predicted LD versus the eLD for all prediction models are displayed in figure 3a–c. Predictive performance was modest and similar for all three models.

Figure 3. Predicted versus measured eLD using the three different approaches. Parameters included were decentration, tilt, age, gender, axial eye length, Rmean, anterior chamber depth, lens thickness, central corneal thickness, white to white and Chang-Waring chord. (a) Prediction using the PLS regression model. (b) Prediction using random forest. (c) Prediction using SVR. eLD, estimated lens diameter; PLS, partial least squares; SVR, support vector regression.

For the partial least squares regression model, an R² of 0.093 was achieved (RMSE: 0.491 mm and MAE: 0.377 mm). Random forest achieved an R² of 0.113 (RMSE: 0.485 mm and MAE: 0.377 mm). Similarly, SVR yielded an R² of 0.118 (RMSE: 0.484 mm and MAE: 0.372 mm). Cross-validation on the training set was comparable to the test set performance (RMSE PLS: 0.513 mm; RMSE random forest: 0.510 mm; RMSE SVR: 0.511 mm).

For all three models, LT, age and AL were among the most important features for prediction (figure 4). Residual spread showed no increase in the short- and long-eye subgroups.

Figure 4. Comparison of predictor importance across models. Permutation importance was calculated as the mean increase in RMSE for all three models, namely PLS regression, random forest and SVR. ACD, anterior chamber depth; AL, axial eye length; CCT, central corneal thickness; CW, Chang-Waring chord; LT, lens thickness; PLS, partial least squares; Rmean, mean anterior corneal radii; RMSE, root-mean-square error; SVR, support vector regression; W2W, white to white.

Discussion

This study evaluated the estimated diameter of the crystalline lens as provided by AS-OCT in a large European study cohort.

An average eLD of 10.18 mm was observed, with relatively little variation between eyes. Only one outlier was found, with an eLD value of 6.84 mm. After careful consideration, no reason for an exclusion was found.

Several studies have focused on the configuration of the crystalline lens, measuring the LD both in vivo and ex vivo using different measurement modalities.^4–7 Using ultrasound, a slightly lower LD of 9.21±0.21 mm was found in a cohort of 79 healthy, non-cataractous patients.² Chen et al analysed 1674 non-cataractous and cataractous patients using the same AS-OCT device used in our study.⁸ They reported slightly different mean lens dimensions: the non-cataractous adolescents measured a mean LD of 9.73±0.29 mm, while the non-cataractous adults measured 9.89±0.30 mm, and the cataractous group measured 9.77±0.78 mm, results lower compared with the findings of this study. They also observed a significant trend for longer AL to have larger LDs. Nagase et al using the same device, compared intraoperative anatomical measurements of the empty capsular bag to the eLD values.⁹ Here, they found an anatomical LD of 10.5±0.4 mm and an eLD of 10.1±0.7 mm, with a significant difference between the two methods. Moreover, only a weak correlation (r=0.31) between the intraoperatively measured LD and the eLD of the device was found, indicating that the estimated parameter cannot be regarded as a validated ground truth. Differences in ethnicity and age as well as choice of measurement methods may explain these discrepancies in mean eLD compared with the results found in our study cohort. In addition, the unvalidated nature of the eLD limits the comparability of this parameter across studies.

With regard to the association with AL, the present study showed a low but significant correlation with AL. The subanalysis of short and long eyes yielded no significant difference in eLD between groups. Waring et al found similar results in a cohort of 470 eyes using a spectral domain-OCT femtosecond-laser imaging system, with no significant correlation between LD and AL in any subgroup.⁷ Likewise, using optical biometry data from the same device used in this study, Rodriguez-Sanchez et al found a low correlation of the reconstructed LD with AL (r=0.19).¹⁰ These findings also support the hypothesis that a large AL does not necessarily correlate with a large LD.

In this study, age was found to correlate with eLD, consistent with the ex vivo findings of Stahnke et al using ultrahigh field MRI.¹¹ Martínez-Enríquez et al also found a positive association of reconstructed LD with age.¹² Age-related changes in lens configuration have to be considered carefully when analysing any single lens parameter, as structural changes lead to a decrease in elasticity and an increase in LT with advancing age. Conversely, accommodation leads to a decrease in LD; therefore, the timing of lens assessment should be taken into account.^{13 14}

Different approaches for LD estimation have been proposed. A study by Erb-Eigner et al using MRI technology looked at the LD both horizontally and vertically in 62 patients with different ocular pathologies.⁶ They also implemented a partial least squares regression approach for LD prediction, which showed globe diameter (measured from equator to equator) and AL for horizontal LD, and globe diameter, distance from the ciliary sulcus and LT as important predictive parameters for vertical LD. Also using MRI, Rozema et al estimated the dimension of the lens from routine biometric parameters using multiple linear regression, predicting the equatorial diameter with an R² of 0.402.¹⁵ Furthermore, Martínez-Enríquez et al developed an ‘eigenlenses’ approach, a principal-component framework aiming to represent the complete three-dimensional shape of the lens developed on ex vivo measurements.¹⁶ Using a similar methodological approach but with a focus on the depth of the equatorial plane in comparison to LD, Romero et al implemented a Python segmentation pipeline to estimate the equatorial plane by the intersection of the anterior and posterior curvature of the crystalline lens as provided by AS-OCT.¹⁷ Subsequently, they looked at the influence of resulting lens parameters on postoperative IOL position prediction, where inclusion of the lens rise from the equatorial plane improved prediction.

The influence of lens parameters on the postoperative outcomes has been investigated further. De Paula et al looked at the influence of LD on postoperative decentration. Here, they were able to show that the crystalline LD and decentration were in low but significant correlation with each other.¹⁸ These results underscore that although LD may play a role, its predictive value for postoperative decentration is limited. Lee et al looked at postoperative decentration and tilt in a cohort of 100 eyes and identified the LD as a factor influencing postoperative tilt, with a large LD being associated with a higher postoperative tilt.¹⁹ Other groups sought to predict the postoperative lens position directly. Satou et al aimed at predicting the postoperative IOL position from parameters obtained from the same AS-OCT used in this study.²⁰ While the eLD was not among the predictors, they evaluated the use of the equatorial depth estimated from the anterior and posterior lens curvature, which proved too error prone to be included in the calculation. In a comparable approach, Langenbucher et al applied 17 machine-learning algorithms using data from the same two devices used in this study to predict the postoperative ACD and the axial position of the equatorial lens plane, finding the benefit of machine learning over a standard multivariate regression model to be limited.²¹

All three models used in this study exhibited notably poor predictive accuracy, as shown by internal validation. This limitation is emphasised by parameter uncertainty, which likely contributes to the models’ poor performance. The feasibility of predicting eLD from biometry therefore appears limited at this stage, underscoring the need for more comprehensive data with further validation before prediction can be considered applicable in clinical practice. The current study did not address the influence on power calculation.

This study has a number of limitations that need to be addressed. One major limitation of this study arises from the nature of the measurement. In the study, the eLD was obtained from a single AS-OCT device, with no assessment of repeatability within patients. Thus far, this device is the only AS-OCT to estimate the LD based on the anterior and posterior curvature of the lens. The value is then provided by extrapolation, which can be adjusted manually using the integrated software of the device. However, this also makes it prone to errors, as the value of the actual LD remains unknown, with the method of evaluation leading to a systematic measurement error²² and subsequent missing validation using other imaging modalities such as MRI or UBM. Here, further studies to investigate the ground truth of the LD are needed. Furthermore, the effect of right/left eye asymmetry has not been evaluated and should be addressed in future studies. Measurements were also not performed under cycloplegia, potentially confounding results with accommodation-related variation of the estimated value. However, as the majority of patients were aged 65 years or older, the influence of accommodation on the analysis is likely to be limited. Lastly, our data set is based on real-world data and included a large variation of short and long eyes as well as eyes with corneal disease. This variation allows for broader analysis but further limits the significance of the prediction models presented in this study.

In summary, this study characterised the eLD of the crystalline lens in a large cohort, showing a mean eLD of 10.18 mm. This study might serve as a reference study for future investigation of the LD.

Data availability statement

Data are available upon reasonable request.