Postoperative intraocular lens tilt from preoperative full crystalline lens geometry using machine learning

Abstract

In cataract surgery, the opacified crystalline lens is replaced by an artificial intraocular lens (IOL), requiring precise preoperative selection of parameters to optimize postoperative visual quality. Three-dimensional customized eye models, which can be constructed using quantitative data from anterior segment optical coherence tomography, provide a robust platform for virtual surgery. These models enable simulations and predictions of the optical outcomes for specific patients and selected IOLs. A critical step in building these models is estimating the IOL's tilt and position preoperatively based on the available preoperative geometrical information (ocular parameters). In this study, we present a machine learning model that, for the first time, incorporates the full shape geometry of the crystalline lens as candidate input features to predict the postoperative IOL tilt. Furthermore, we identify the most relevant features for this prediction task. Our model demonstrates statistically significantly lower estimation errors compared to a simple linear correlation method, reducing the estimation error by approximately 6%. These findings highlight the potential of this approach to enhance the accuracy of postoperative predictions. Further work is needed to examine the potential for such postoperative predictions to improve visual outcomes in cataract patients.

Fig. 1.

Flow chart of the methodology to estimate the IOL tilt from preoperative measurements, that includes the 3-D model construction, quantification (for obtaining the geometrical features and the ground truth that will feed the machine learning algorithm) and feature selection/learning processes. In the 3-D model construction, the anterior surface of the cornea (blue), posterior surface of the cornea (red), anterior surface of the crystalline lens/IOL (yellow), and posterior surface of the crystalline lens/IOL (purple) are represented. In the preoperative models, the full shape of the crystalline lens is also shown (black).

Fig. 2.

Preoperative (top) and postoperative (bottom) IOLMaster 700 OCT images (meridian at 300°, OD, Female, 90 years old), showing the crystalline lens and the implanted IOL (Clareon CNA0T0 by Alcon, 23.5 D) respectively.

Fig. 3.

Preoperative 3-D eye model construction. Surface segmentation, distortion correction, and registration were performed to generate 3-D models of the eye. The full shape of the crystalline lens was estimated using the eigenlenses method [34,35]. The processes for obtaining 3-D postoperative models are the same, excluding the full shape estimation of the crystalline lens.

Fig. 4.

Definition of some of the features from 3-D preoperative models.

Fig. 5.

Definition of the IOL tilt magnitude and direction from the 3-D postoperative models. These are the variables to be predicted.

Fig. 6.

Polar plots for right (left column) and left (right column) eyes, where the radial distance to the center represents the tilt magnitude in degrees, while the angle represents the tilt direction. A) Preoperative natural crystalline lens tilt; B) Postoperative IOL tilt. Outliers are shown in red.

Fig. 7.

Scatterplot with best linear regression lines, marginal histograms, and 95% confidence intervals (CI) between preoperative tilt (the tilt of the natural crystalline lens before the surgery) and postoperative tilt (the tilt of the IOL implanted). A) Tilt magnitude. B) Tilt direction. Pearson correlation coefficients (ρ) and the p-value for testing the hypothesis of no correlation are also shown. Outliers (not taken into account for fitting the model) are shown in red color (some outliers are not visible because they are out of the range represented in the axes).

Fig. 8.

Scatterplot with best linear regression lines, marginal histograms, and 95% confidence intervals (CI) between right eyes (OD) and left eyes (OS). Top row: preoperative measurements; bottom row: postoperative measurements. A) Tilt magnitude; B) Tilt direction. 97 patients with paired eyes are used in the analysis. Pearson correlation coefficients (ρ) and the p-value for testing the hypothesis of no correlation are also shown.

Fig. 9.

Feature selection process, quantifying the decrease of MSE es as new features are included in the estimation. A) Postoperative tilt magnitude estimation. The ranking of Features is: 1) Preoperative tilt magnitude; 2) Equatorial Plane Position (EPP), obtained from the full shape of the crystalline lens; 3) Preoperative tilt direction; 4) Radius of curvature of anterior cornea (RAC); 5) Gender; 6) Vitreous Chamber Depth (VCD); B) Postoperative tilt direction estimation. The ranking of features is: 1) Preoperative tilt direction; 2) Laterality of the eye (OD-OS); 3) $a_4$ eigenlens coefficient, that indicates asymmetric changes of the shape of the lens; 4) $a_1$ eigenlens coefficient, related with the size of the crystalline lens; 5) # days (Number of days since operation, defined as the number of days from surgery to postoperative scan); 6) ACD (Anterior Chamber Depth). Error bars represent STD across experiments. Asterisks indicate statistically significant difference between mean MAE for consecutive number of features (i.e., comparing consecutive states of the feature selection algorithm). Paired t-test, p < 0.05.