Determination of the estimated lens position of an intraocular lens using three-dimensional anterior segment geometry and machine learning

Abstract

A method for determining the relationship between measured variables of the anterior segment in a patient's eye pre-operatively and the post-operative position, and optionally tilt, of the implanted intraocular lens (IOL) is described, based on quantitative optical coherence tomography imaging of the eye of a patient and a machine learning architecture to determine the best regression model. Formulas are further described obtained using such method to determine the Estimated Lens Position (ELP), and optionally tilt, from measured variables in a patient pre-operatively to incorporate in IOL power calculation formulas or ray-tracing based IOL power selection.

Description

DETERMINATION OF THE ESTIMATED LENS POSITION OF AN INTRAOCULAR LENS USINGTHREE-DIMENSIONAL ANTERIOR SEGMENT GEOMETRY AND MACHINE LEARNINGCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims the benefit of US Provisional Application No. 63 / 599,772 filed November 16, 2024 and US Provisional Application No. 63 / 644,171 filed May 8, 2024, the disclosures of which are hereby incorporated by reference herein in their entireties.BACKGROUND

[0002] The replacement of the natural crystalline lens of the eye by an artificial lens (so-called intraocular lens, IOL) is standard practice to correct for the age-related crystalline lens opacification (cataract), or even at earlier ages from congenital or traumatic cataract. The procedure can also be applied while the crystalline lens is still transparent, although generally unable to reshape to focus (presbyopia), as a refractive procedure.

[0003] In all cases, a primary goal of the procedure is meeting the refractive target, i.e., that the IOL in combination with the cornea, focuses the images of the outside world (generally distance images) on the patient’s retina.

[0004] Different strategies have been proposed to determine the power of the IOL to be implanted (see Figure 1 for a chronological evolution of the various paraxial, also called vergence, and ray tracing formulas which have been proposed for determining the IOL power estimation). Along with comeal power and axial length, the estimation of where the IOL will sit axially (i.e., Estimated Lens Position (ELP)) is critical in what the effective power should be, and consequently in the accuracy of refraction correction. Accordingly, it would be desirable to provide improved methods for providing an estimated lens position for an IOL to be implanted into a patient’s eye, for use in determining the selected power of the IOL to be implanted in the patient.SUMMARY

[0005] One embodiment of the disclosure is directed towards a method of determining a post-operative estimated lens position (ELP) of an intraocular lens (IOL) in an eye of a patient, for use in selecting an IOL for insertion into the eye, comprising the steps of: generating an ELP equation based on a machine learning analysis of a data setincluding selected parameters defining pre-operative ocular geometric features of a plurality of eyes and post-operative IOL positioning in the plurality of eyes, wherein the selected parameters include at least one parameter based on a full shape of the crystalline lens of the eye; obtaining data defining pre-operative ocular geometric features of an eye of a patient from pre-operative in vivo quantitative optical coherence tomography imaging of the eye; and determining a post-operative ELP for the eye of the patient based on the ELP equation and the data obtained from pre-operative in vivo quantitative optical coherence tomography.

[0006] In particular embodiments, the data set employed in the machine learning analysis may include pre-operative 3 -dimensional biometric data obtained from quantification of anterior segment OCT including in vivo visible portions of the crystalline lens, and the method may further comprise determining the at least one parameter based on a full shape of the crystalline lens based on at least one eigenlens deformation pattern coefficient relative to an average lens shape obtained from a training set of isolated crystalline lenses.

[0007] In further particular embodiments, the ELP equation may be generated further based on where the data set includes at least one IOL type parameter.

[0008] In further particular embodiments, a post-operative estimated lens tilt of the IOL in the eye of the patient may further be determined, for use with the ELP in selecting an IOL for insertion into the eye, comprising the further steps of: generating an estimated IOL tilt equation based on a machine learning analysis of a data set including selected parameters defining pre-operative ocular geometric features of a plurality of eyes and post-operative IOL tilt in the plurality of eyes; obtaining data defining pre-operative ocular geometric features of an eye of a patient from pre-operative in vivo quantitative optical coherence tomography imaging of the eye; and determining a post-operative estimated IOL tilt for the eye of the patient based on the estimated IOL tilt equation and the data obtained from pre-operative in vivo quantitative optical coherence tomography. In such embodiments, the selected parameters may include at least one parameter based on a full shape of the crystalline lens of the eye.

[0009] In further embodiments, the methods described in the present disclosure may further comprise selecting an IOL based at least in part on the determined post-operative ELP, and inserting the selected IOL into the eye of the patient.BRIEF DESCRIPTION OF THE DRAWINGS

[0010] FIG. 1 is a chart depicting chronological evolution of various IOL power selection formulas.

[0011] FIGs. 2A and 2B illustrate a 3D OCT anterior segment imaging of an eye (FIG. 2A) and a corresponding crystalline lens shape reconstruction (FIG. 2B) based thereon.

[0012] FIG. 3. is an illustration of six eigenlens deformation pattern representations of the crystalline lens.

[0013] FIG. 4 is a schematic diagram of the methodology employed in one embodiment of the disclosure.

[0014] FIG. 5 is a graph showing how the MAE estimation error decreases as each of 4 selected features is included in a GPR regression method employed in an embodiment of the disclosure.DETAILED DESCRIPTION

[0015] The following description is not to be taken in a limiting sense but is given solely for the purpose of describing the broad principles of the disclosure. Specific embodiments may be described by way of example.

[0016] Referring again to FIG. 1, the so-called second-generation (Holladay 1, SRK / T) and third-generation (Holladay 2, Haigis) IOL power formulas use generally limited inputs on the patient eye (corneal curvature K, and axial length AL) and assumptions regarding the relation between anterior and posterior corneal shape (by the so-called keratometric index). Most notably, they differ on the way that the Estimated Lens Position (ELP) is calculated. Although in most cases (except for the Olsen Formula, that also includes crystalline lens thickness) the ELP is estimated from K, AL, and preoperative anterior chamber depth (ACD), the different formulas include different adjustment factors and optimization coefficients that attempt to improve the accuracy of the formulas for different eye lengths. Those coefficients can be either obtained from regression methods using population data or using theoretical equations (like in the Barrett Universal formula II, which also retains information on the IOL principal plane). An additional required factor in these formulas is the so-called A-constant, or moregenerally lens factor, which are constants generally given by the manufacturer for each IOL platform (and generally empirically modified by each surgeon over time) to adjust the calculation.

[0017] An alternative to the traditional vergence formulas for IOL power calculation are ray tracing formulas. The rationale behind these formulas is to construct an eye model with information of the cornea, intraocular distances, and lens geometry, and perform virtual ray tracing. An image quality metric (i.e., extent of the spot diagram, visual Strehl ratio, etc.) is defined and the IOL power that optimizes that metric (therefore optimizing focusing in the retina) is selected. The eye models used in the ray tracing method can be customized to each subject, introducing the best anterior and posterior corneal shapes which can be obtained from Scheimpflug or OCT-based corneal topography. Ray tracing performed on pseudophakic custom model eyes (including corneal shape, measured biometry and ocular axes, and IOL geometry) has shown to reproduce to large degree of accuracy both refractive error and the high order aberration, suggesting that this method, instead of paraxial calculations, has the ability to capture the effect of the individual differences in the ocular optics to calculate the IOL power in particular, and selection of the optimal IOL design at the patient level.

[0018] However, also in the ray tracing method, lens position needs to be estimated and incorporated into the eye models. Therefore, accurate ELP is critical both in traditional and ray tracing based formulas.

[0019] The development of 3D anterior segment imaging techniques provides access to biometric information relevant for intraocular lens implantation. Following application of fan and optical distortion corrections, it is possible to obtain fully quantified data of the topographies of the cornea and the crystalline lens (Ortiz et al., 2009). Furthermore, previous reports have presented methodology to quantify the shape of the crystalline lens even beyond the margins of the eye’s pupil, where the signal is blocked by the iris (Martinez-Enriquez et al., 2016). FIGs 2A and 2B, adapted from Martinez-Enriquez et al., 2016, e.g., show 3D OCT anterior segment imaging (FIG. 2A, where only portions I la and 1 lb of the crystalline lens which are not blocked by the eye’s pupil 12 are visible based on the OCT imaging, where the cornea 13 is also imaged) and crystalline lens shape reconstruction (FIG. 2B, where the entire crystalline lens 11 shape is reconstructed based on the imaged portions) images, where extrapolation algorithms were developed and trained on a data set of isolated crystalline lenses from donor eyes, and demonstrated invivo, both in young patients with different amounts of myopia, as a function of accommodation (focusing near and far) as well as in cataract eyes.

[0020] Additional methods have been proposed to represent with great accuracy the full shape of the crystalline lens using a basis (eigenlenses) with a limited number of coefficients (Martinez-Enriquez et al., 2020), which allows representation of any lens as the addition of an average lens (the mean shape over a training set of lenses) and a linear combination of typical deformations from this mean shape. As shown in FIG. 3, adapted from Martinez-Enriquez et al., 2020, e.g., 6 different eigenlens representations of the crystalline lens are depicted, where the eigenlenses represent the most common “deformation patterns” that can be found in a training set of 133 isolated crystalline lenses, with respect to the average lens shape. Thanks to the richness of the training set (that includes lenses of ages ranging from 0 to 71 y / o), eigenlenses can represent efficiently the human crystalline lens shapes that can be found in nature. The first eigenlens k=l describes changes in the size of the lens (the most “common” deformation), while the second eigenlens k=2 describes changes in the aspect ratio (i.e., lenses more “stretched” or rounded). The third (k=3) and fourth eigenlenses relate to asymmetric changes in the X or Y directions, and the fifth (k=5) and sixth (k=6) eigenlenses relate to fine changes in the shape of the surfaces (related to the aspehericity of conicoids or with rotationally symmetric Zemike polynomials). Eigenlenses representation is compact, needing only 6 coefficients to capture 96% of the variance in shape of the training set of lenses. Thanks to this compaction ability, eigenlenses are useful to estimate the full shape of the lens in vivo from its central part visible through the pupil (Martinez-Enriquez et al., 2020). A greater or fewer umber of eigenlenses may be employed if desired based on the trade-off between obtaining a compact representation (with a smaller number of eigenlenses) and capturing relevant geometrical information of the lenses to achieve an accurate representation.

[0021] These methods of characterization of the crystalline lens shape and position can also be used on OCT images acquired with tomography systems (for example the lOLMaster 700 by Zeiss or the Heidelberg Anterion OCT), allowing access to comprehensive pre-operative data on the crystalline lens, including parameters such as lens thickness (LT), anterior and posterior lens curvature (RAL and RPL), equatorial lens diameter (DIA), lens volume (VOL), lens surface area (LSA) or equatorial plane position (EPP), and alternatively a set of eigenlens coefficients describing the shape of the crystalline lens. Given that in a standard cataract procedure the IOL is implanted insidethe capsular bag of the lens, and given the large variability of the crystalline lens dimensions in the population, the pre-operative lens dimensions and position plays a fundamental role in ELP.

[0022] In prior work (Martinez-Enriquez et al. 2018, Martinez-Enriquez et al. 2017), based on OCT 3-D biometric measurements pre- and post- cataract surgery on 12 patients, using a custom developed anterior segment OCT imaging system, relations between the post-operative measured lens position and pre-operative lens parameters were obtained. In one expression ELP depends on the preoperative anterior chamber depth (ACD) and EPP / LT. In another expression ELP depends on LT and LSA / VOL, obtained using a linear correlation model between ELP and the pre-operative parameters (found using brute-force combinations of parameters).

[0023] In recent times machine learning has been proposed to estimate the IOL power, benefiting from large availability of data made accessible through electronic records and the advent of supervised machine learning methods, which use a subset from the entire data set for training and can generalize to predict outcomes. Some reports describe Artificial Intelligence (Al) approaches for optimization of the constants of the traditional formulas. For example, Mori et al. 2021 used support vector regressor to optimize the Haigis and SRK / T formulas. Others (Hill-RBF) use standard machine learning approaches to directly predict IOL power from standard biometric input parameters, such as Hill et al. who used Radial Basis Function (RBF) or Sramka et al. who instead used Support Vector Machine Regression model (SVM-RM) and Multilayer Neural Network Ensemble model (MLNN-EM). Gradient Boosting (XGBoost) algorithms have also been used to improve the prediction accuracy in highly myopic eyes.

[0024] Some authors have proposed undisclosed Al methods to improve several steps in the calculation. For example, the Kane formula proposes to use Al to predict IOL position, using Anterior K, K, ACD, and gender as required entry points, and LT and corneal thickness as optional parameters. The PEARL -DGS formula (Postoperative spherical Equivalent prediction using ARtificial intelligence and Linear algorithms, developed by Debellemaniere, Gatinel, and Saad) uses thick lens power optical calculations and Al methods to predict the theoretical internal lens position (TILP) back- calculated from postoperative refractive data. The last version of the Ladas Superformula proposes to use Al methods to select the optimal formula for IOL power calculations from existing equations.

[0025] While all prior proposed methods related to the use of machine learning approaches to optimize IOL selection may rely on the power of large data sets, they are typically ultimately based on the use of demographic and limited uni-dimensional biometric data, and generally represent a blind, black-box approach to the calculation.

[0026] The present disclosure more particularly describes a novel methodology of leveraging the three-dimensional biometric data obtained from quantification of anterior segment OCT, in particular crystalline lens full shape parameters, together with the power of machine learning methods to extract complex relations between variables. In particular, supervised machine learning is used to relate pre-operative biometric, crystalline lens parameters and IOL type with post-operative position to provide the most accurate, anatomically informed ELP equations, for use cither in traditional formulas or ray tracing IOL estimation.

[0027] The present disclosure describes the generation of ELP equations based on selected parameter correlations for estimation of the post-operative position of the IOL (ELP) given 3-D biometric features of the eye using regression methods, in particular ridge models (best linear model selected from different methods tested) and Gaussian process regression (GPR) (best non-linear model). In specific embodiments a 5-fold cross- validation approach was used (i.e., splitting the sample in 5 groups, using 4 for training and 1 for test) and the experiment was repeated 200 or 1000 times. The relevant features were selected using feature selection methods, including permutation feature in Feedforward neural networks, highest mean absolute coefficients in ridge model, minimum redundancy maximum relevance (fsrmrmr), univariate feature ranking for regression using F-tests (fsrftest), and sequential forward / backward feature selection, as well as using expert knowledge (based on medical expert’s experience and knowledge on which features tend to be most important). Lens position estimation advantageously based on a single estimator derived from an eye’s anatomical parameters, patient demographic data, and IOL type.

[0028] Embodiment 1

[0029] In a first embodiment, a dataset was employed which consisted of 61 eyes from patients undergoing cataract surgery at the Flaum Eye Research Institute, and each eye had, originally, 62 identified parameters, alternatively designated as features, associated therewith, including 16 pre-operative clinical features (features obtained in the clinic or directly output by the IOL Master 700, including patient age, sex, the laterality of the eye,the pupil size, and the IOL model), 23 pre-operative geometrical features obtained from OCT (geometric features of the eye obtained from OCT images with custom designed programs, such as the axial length, comeal thickness, or the crystalline lens curvature), and 23 pre-operative crystalline lens full shape features obtained from OCT (features including crystalline lens full shape features, such as the volume of the lenses or the coefficients of the eigenlenses method, where eigenlenses coefficient were determined in accordance with the methodology described in Martinez-Enriquez et ah, 2020).

[0030] Specifically, the set of features employed in this first embodiment included the following.

[0031] Clinical Features(1) Sex (1M2F): Male or Female (categorical).(2) Laterality (1OD2OS): Right eye or left eye (categorical).(3) AgeAtTimeOfOperationyear: Age of the patient.(4) lOLModel (1SN60WF2CNA0T03MX60EUS): IOL Model implanted (categorical).(5) lOLPowerlnsertedD: IOL Powerlnserted, in Diopters.(6) AxialLengthmm lOLMaster (ALioLMaster): Axial length obtained directly from the IOL Master 700 system in millimeters.(7) PreopKl : Keratometry. Highest Radius of curvature meridian in cornea, in Diopters.(8) Preop KI Axis: Keratometry. Angle of the highest Radius of curvature meridian in cornea in degrees.(9) Preop K2: Keratometry. Lowest Radius of curvature meridian in cornea, in Diopters.(10) PreopK2Axis: Keratometry. Angle of the lowest Radius of curvature meridian in cornea, in degrees.(11) Sphere: Preoperative refraction of the patient’s eye, in Diopters.(12) Cyl: Preoperative astigmatism of the patient’s eye, in Diopters.(13) SphericalEquiv: Preoperative spherical equivalent of the patient’s eye, in Diopters.(14) Number of days to post-op scan: Num days from surgery to postoperative scan.(15) Pupil size: Preoperative pupil size, in millimeters.(16) Radius of curvature of Anterior Cornea (RAC): Mean radius of curvature of the anterior surface of the cornea, in millimeters.

[0032] Geometrical Features from OCT(17) Corneal Thickness (CT): Corneal thickness in millimeters.(18) ACD: Anterior chamber depth in millimeters.(19) LT: Crystalline lens thickness in millimeters.(20) Vitreous chamber depth (VCD): Vitreous chamber depth in millimeters.(21) Axial Length (ALOCT): Axial length, obtained from OCT images in millimeters.(22) AL not corrected: Axial length, obtained from OCT images, without correction with different indices of refraction (i.e., using an equivalent index of refraction) in millimeters.(23) std_AL_non_corrected_eyes: Standard deviation of the AL not corrected across meridians in millimeters.(24) med RAC eyes: Mean Radius of curvature of the anterior surface of the cornea across 2-D meridians (i.e., best circle fitting. Fitting diameter=3mm) in millimeters.(25) med RPC eyes: Mean Radius of curvature of the posterior surface of the cornea across 2-D meridians (i.e., best circle fitting. Fitting diameter=3mm) in millimeters.(26) med_RAL_eyes: Mean Radius of curvature of the anterior surface of the crystalline lens across 2-D meridians (i.e., best circle fitting. Fitting diameter=3mm) in millimeters.(27) med RPL eyes: Mean Radius of curvature of the posterior surface of the crystalline lens across 2-D meridians (i.e., best circle fitting. Fitting diameter=3mm) in millimeters.(28) med_RAC_eyes_Diam2: Mean Radius of curvature of the anterior surface of the cornea across 2-D meridians (i.e., best circle fitting. Fitting diameter=6mm) in millimeters.(29) med_RPC_eyes_Diam2: Mean Radius of curvature of the posterior surface of the cornea across 2-D meridians (i.e., best circle fitting. Fitting diameter=6mm) in millimeters.(30) med_RAL_eyes_Diam2: Mean Radius of curvature of the anterior surface of the crystalline lens across 2-D meridians (i.e., best circle fitting. Fitting diameter=6mm) in millimeters.(31) med_RPL_eyes_Diam2: Mean Radius of curvature of the posterior surface of the crystalline lens across 2-D meridians (i.e., best circle fitting. Fitting diameter=6mm) in millimeters.(32) RAC_3D: Radius of curvature of the anterior surface of the cornea from the 3-D models (i.e., best sphere fitting. Fitting diameter=3mm) in millimeters.(33) RPC 3D: Radius of curvature of the posterior surface of the cornea from the 3-D models (i.e., best sphere fitting. Fitting diameter=3mm) in millimeters.(34) RAL 3D: Radius of curvature of the anterior surface of the crystalline lens from the 3-D models (i.e., best sphere fitting. Fitting diameter=3mm) in millimeters.(35) RPL_3D: Radius of curvature of the posterior surface of the crystalline lens from the 3-D models (i.e., best sphere fitting. Fitting diameter=3mm) in millimeters.(36) RAC_3D Diam2: Radius of curvature of the anterior surface of the cornea from the 3-D models (i.e., best sphere fitting. Fitting diameter=6mm) in millimeters.(37) RPC_3D_Diam2: Radius of curvature of the posterior surface of the cornea from the 3-D models (i.e., best sphere fitting. Fitting diameter=6mm) in millimeters.(38) RAL 3D Diam2: Radius of curvature of the anterior surface of the crystalline lens from the 3-D models (i.e., best sphere fitting. Fitting diamctcr=6mm) in millimeters.(39) RPL_3D_Diam2: Radius of curvature of the posterior surface of the crystalline lens from the 3-D models (i.e., best sphere fitting. Fitting diameter=6mm) in millimeters.

[0033] Full shape of the crystalline lens geometrical features(40) VOL_eigen_lenses: Volume of the crystalline lens, from the full shape estimated using eigenlenses method in cubic millimeters.(41) LSA_eigen_lenses: Surface area of the crystalline lens, from the full shape estimated using eigenlenses method in square millimeters.(42) DIA_eigen_lenses: Equatorial diameter of the crystalline lens, from the full shape estimated using eigenlenses method in millimeters.(43) EPP eigen lenses: Equatorial plane position of the crystalline lens, from the full shape estimated using eigenlenses method in millimeters.(44) LT_eigen_lenses: Crystalline lens thickness, from the full shape estimated using eigenlenses method in millimeters.(45) Coef_eigenlenses, al: First eigenlens coefficient.(46) Coef_eigenlenses, a2: Second eigenlens coefficient.(47) Coef_eigenlenses, a3: Third eigenlens coefficient.(48) Coef_eigenlenses, a4: Fourth eigenlens coefficient.(49) Coef_eigenlenses, a5: Fifth eigenlens coefficient.(50) Coef_eigenlenses, a6: Sixth eigenlens coefficient.(51) Coef_eigencenters, cl: First eigencenter coefficient.(52) Coef_eigencenters, c2: Second eigencenter coefficient.(53) Coef_eigencenters, c3: Third eigencenter coefficient.(54) Cocf_eigcnccntcrs, c4: Fourth eigencenter coefficient.(55) Coef_eigencenters, c5: Fifth eigencenter coefficient.(56) Coef_eigencenters, c6: Sixth eigencenter coefficient.(57) EPP_eigen_lenses2: Equatorial plane position of the crystalline lens, calculated in a different way, from the full shape estimated using eigenlenses method in millimeters.(58) LT_iovs: Crystalline lens thickness, from the full shape estimated using IOVS method in millimeters.(59) VOL iovs: Volume of the crystalline lens, from the full shape estimated using IOVS method in cubic millimeters.(60) LSA_iovs: Surface area of the crystalline lens, from the full shape estimated using IOVS method in square millimeters.(61) DIA iovs: Equatorial diameter of the crystalline lens, from the full shape estimated using IOVS method in millimeters.(62) EPP iovs: Equatorial plane position of the crystalline lens, from the full shape estimated using IOVS method in millimeters.

[0034] In such feature sets, while the first through sixth eigenlens coefficients al-a6 relate to variations in the overall shape of the crystalline lens, the first through sixth eigencenter coefficients cl-c6 relate to the shape of the crystalline lens only in the central optical region of the lens (i. e. , the lens portion visible through the pupil which can be imaged by OCT anterior segment imaging).

[0035] LABELS (VARIABLES TO BE PREDICTED)IOL position: Defined as the distance between posterior cornea surface and anterior IOL surface in the postoperative models, in millimeters.

[0036] The optimization metric is the average mean absolute error (MAE) in pm between estimated and actual lens position in the test set. The average is calculated over 5-fold cross validation repeated 200 / 1000 times.

[0037] FIG. 4 shows a schematic diagram of the methodology employed. The process of obtaining the input features from OCT images involves: (1) automatic segmentation of the surfaces of interest; (2) 3-D model construction, including conversion from pixels to millimeters using calibration data, correction of the fan and the optical distortion, registration of the different meridians to obtain the 3-D model within the pupil, and crystalline lens full shape estimation from its central part visible through the pupil; and (3) quantification of the parameters of interest. Note that the quantification step shows an example of an input feature set after feature selection. Significantly, geometrical features describing the surfaces and the full shape of the crystalline lens are used in a machine learning method for estimation of the IOL position. Furthermore, features based on the IOL model / type are included in the estimation algorithm, so that it can learn how the final IOL position depends on the IOL design.

[0038] After performing feature selection, 5 sets of features were obtained that could be of interest. For each group of features, two different estimators relating ELP with measured pre-operative parameters (features) were obtained applying the method described above (see above brief explanation of the different features used in the formulas). Specifically, for each set of features we trained GPR and ridge regression models.

[0039] Below we show the best Ridge Regression models, expressed as equations (formulas) for different sets of an eye’s features.

[0040] Regarding GPR, we consider the following model [Rasmussen et al. 2018, Statistics and Machine Learning Toolbox Matlab]:where / (x) is a zero mean Gaussian Process, are a set offixed basis functions that transform the original feature vector x, and β are basis function coefficients.

[0041] In our experiments, we chose a constant basis function h(x) and an exponential kernel, defined as follows:where σiis the characteristic length scale and is the Euclideandistance between xiand xj. Thus, the model is completely defined by the variance ofnoise ofi , the P coefficients, and the hyperparameters of the kernel function oy and <T;, which are obtained by training the model and are specified below for each case.

[0042] Trained Regression Model Results

[0043] Example Formula 1 (using 9 features: RAC, ALOCT, IOL type (lOLModell, IOLModel2 or IOLModel3), ACD, VCD, CT, LT, RAL 3D, and RPL 3D). Note that lOLModell refers to the IOL model SN60WF by Alcon, IOLModel2 refers to the model CNA0T03 by Alcon, and IOLModel3 refers to the model MX60EUS by Bausch and Lomb.

[0044] Formula LA. Ridge:ELP = 4.2773 - 0.0584 ■ lOLModell + 0.0164 ■ IOLModel2 + 0.2677 ■ IOLModel3- 0.0219 ■ RAC + 0.1324 ■ ALOCT+ 0.2814 ■ ACD - 0.0193 ■ VCD- 0.0159 ■ CT + 0.1255 ■ LT + 0.0659 ■ RAL_3D - 0.025 ■ RPL_3D

[0045] Formula LB, GPR (optimal trained parameters):

[0046] Example Formula 2 (using 7 features: RAC, ALOCT, IOL type, ACD, VCD, CT, and LT).

[0047] Formula 2.A. Ridge:ELP = 4.2745 - 0.0958 ■ lOLModell + 0.0115 ■ IOLModel2 + 0.2820 ■ IOLModel3- 0.0110 ■ RAC + 0.1306 ■ AL0CT+ 0.3042 ■ ACD - 0.0133 ■ VCD— 0.0365 ■ CT + 0.0875 ■ LT

[0048] Formula 2,B, GPR (optimal trained parameters):

[0049] Example Formula 3 (using 10 features: RAC, ALOCT, IOL type, ACD, VCD, CT, LT, RAL 3D, RPL 3D, and DIA eigen lenses).

[0050] Formula 3.A. Ridge:ELP = 4.2590 - 0.0716 ■ lOLModell - 0.0140 ■ IOLModel2 + 0.2791 ■ IOLModel3- 0.0179 ■ RAC + 0.1306 ■ AL0CT+ 0.3053 ■ ACD - 0.0135 ■ VCD- 0.0014 ■ CT + 0.1081 ■ LT + 0.0318 ■ RAL_3D - 0.1146 ■ RPL_3D+ 0.0929 ■ DIA_eigen_lenses

[0051] Formula 3.B, GPR (optimal trained parameters):

[0052] Example Formula 4 (using 7 features, selected with expert knowledge: RAC, ALOCT, IOL type, ACD, RAL 3D, RPL 3D, al eigenlens coefficient (i.e. , Formula 1 removing CT, VCD and LT, and including al)). Note that al eigenlens coefficient was determined by Martinez-Enriquez et al., 2020.

[0053] Formula 4,A, Ridge:ELP = 4.28 - 0.0781 ■ lOLModell - 0.0147 ■ IOLModel2 + 0.3061 ■ IOLModel3- 0.0174 ■ RAC + 0.1113 ■ AL0CT+ 0.2875 ■ ACD + 0.0446 ■ RAL_3D- 0.1104 ■ RPL_3D - 0.1234 ■ a±

[0054] Formula 4.B. GPR (optimal trained parameters):

[0055] Example Formula 5 (using 7 features, selected with forward / backward feature selection algorithm: ALioLMaster, IOL type, ACD, cl eigencenter coefficient, EPP iovs, Cyl, VOL-iovs)). Note that cl cigcnccntcr coefficient was determined by Martinez- Enriquez et aL, 2020, and EPP iovs and VOL iovs were determined by Martinez-Enriquez et al, 2016.

[0056] Formula 5.A. Ridge:

[0057] Formula 5.B. GPR (optimal trained parameters):

[0058] Table 1 shows the mean absolute error MAEs in the estimation of IOL position with each set of features, using Ridge and GPR methods.

[0059] TABLE 1* Standard deviation values across eyes not available.

[0060] The error in the ELP obtained from the machine learning based formulas is significantly smaller and in many instances about one-half to two-thirds of that obtained from the IOL position estimations in standard formulas (e.g., 256±234 pm using SRK / T and 201±176 pm using Haigis). In particular, Formula 4 including use of a first cigcnlcns coefficient al based on overall shape of the crystalline lens provided best obtained MAE values.

[0061] Based on the smaller MAE values, an increased accuracy on postoperative refraction after surgery may be expected to be obtained when using the described IOL position estimation method in standard IOL power selection or ray tracing methods. Specifically, in previous work (Martinez-Enriquez et al 2018), it was shown that by reducing the error approximately the same amount that we have obtained in this work in comparison with the standard SRK / T (—130 microns), the proposed approach would result in a different preoperative selection of IOL power in approximately the 40 % of eyes, following the same selection criteria by the same surgeon.

[0062] Embodiment 2

[0063] In a second embodiment, a dataset was employed which consisted of 126 eyes from 103 patients (obtained from an initial set of 164 eyes from 130 patients, after discarding eyes with pupils smaller than 3 mm) implanted with 5 different IOL models (AcrySof, Alcon, n=28; Clareon, Alcon, n=56; Acrysoft Vivity, Alcon, n=l 1; enVista, B&L, n=8; Tecnis, J&J, n=23).

[0064] Similar to the methodology shown in Fig. 4, a further estimation of the lens position is presented using 4 features selected using sequential feature selection and the GPR regression method. The feature selection starts with an empty set of features and includes, at each iteration, the feature that minimizes the MAE in the lens position estimation using test data. The average is calculated over 5-fold cross validation repeated 200 times. The specific feature ranking (features ordered as a function of their importance in the estimation) employed in this second embodiment of the disclosure is:1st feature: Anterior chamber depth (ACD);2nd feature: IOL model (lOLmod);3rd feature: First eigenlens coefficient (al, related with the general size of the lens); 4th feature: Axial length (AL).

[0065] FIG. 5 shows how the MAE estimation error decreases as each of the selected features is included. Table 2 shows the mean absolute error (MAE) between estimated and actual lens position in a test set, Maximum error (Max), and number of eyes in which the estimation error was higher than 200 um (Num>200), for estimates obtained in accordance with this Embodiment 2 (ELP-AI) methodology versus comparison estimates made with prior proposed estimators. In particular, the MAE obtained with ELP-AI was shown to be statistically significantly lower (ANOVA p<0.05, Bonferroni) than with SRK7T, Haigis, Hoffer Q, and Intersection approach (which extrapolates the lens periphery surfaces blocked by the iris using circle fitting of the visible portions of the anterior and posterior surfaces of the lens, with the equatorial diameter obtained from their intersection and used as the ELP).

[0066] TABLE 2

[0067] The second embodiment thus presents further advantageous estimation results using another set of data and specific set of features, wherein full shape crystalline lens features quantified from OCT images in combination with machine learning algorithms improved the accuracy of IOL position estimation in cataract surgery, which is critical for improving refractive outcomes.

[0068] Embodiment 3

[0069] In addition to providing ELP, the OCT imaging and machine learning techniques described herein employing selected parameters including at least one parameter based on a full shape of the crystalline lens of the eye may be further employed to predict post-operative IOL tilt. This may be further significant as resulting degree of post-operative tilt can impact the optical performance of intraocular lenses.

[0070] In a third embodiment, a dataset was employed which consisted of 96 eyes (obtained from an initial set of 129 eyes from 94 patients, after discarding eyes with pupils smaller than 3 mm) where the eyes were measured prc / post-opcrativcly with Swept Source OCT (IOLMaster700, Zeiss, 6 meridians). IOL tilt was estimated after cataract surgery using the swept-source optical coherence tomography (SS-OCT) imaging of the crystalline lens and machine learning (ML) algorithms, where pre-operative features were used to predict post operative IOL tilt. Specifically, the tilt magnitude and tilt direction, as defined in Himschall N, et al. “Prediction of postoperative intraocular lens tilt using swept-source optical coherence tomography,” J Cataract Refract Surg. 2017;43(6):732- 736. doi: 10. 1016 / j .jcrs.2017.01.026, were predicted.

[0071] From the raw preoperative OCT images, automatic surface extraction (segmentation) was performed and 3-D models of the anterior segment of the eye werethen obtained, after applying distortion correction, registration, and full-shape estimation processes.

[0072] From the obtained preoperative 3-D models, 64 geometrical features were quantified (62 features defined above in Embodiment 1, in addition to pre-operative tilt magnitude and pre-operative tilt direction, where both the pre-operative tilt parameters for the natural crystalline lens and the post-operative tilt parameters for the IOL are similarly characterized as defined in Hirschall N, et al. as noted above). All of these features are candidate inputs to the machine learning algorithm. The most relevant features are chosen using a sequential feature selection algorithm.

[0073] From the raw postoperative OCT images, automatic surface extraction (segmentation) was performed and 3-D models of the cornea and intra ocular lens (IOL) were then obtained after applying distortion correction and registration processes.

[0074] From the obtained postoperative 3-D models, post-operative tilt magnitude and post-operative tilt direction were obtained, that are used as the ground truth for training two different estimation methods.

[0075] Feature rankings (features ordered as a function of their importance in the estimation) were obtained for estimating each of the IOL tilt magnitude and tilt orientation.

[0076] In this third embodiment, the relevant features selected for the estimation of post-operative tilt magnitude are:1. Pre-operative tilt magnitude (TM).2. Crystalline lens equatorial plane position (EPP eigenlenses).3. Pupil size.4. Radius of curvature of anterior cornea (RAC).5. Age of the patient.

[0077] In this third embodiment, the relevant features selected for the estimation of post-operative tilt direction are:1. Pre-operative tilt direction (TD).2. Pupil size.3. Estimated full crystalline lens size (eigenlens coefficient al).4. Pre-operative tilt magnitude.

[0078] The estimation error results are presented using ridge models, with the features indicated above as input features, 100 independent experiments and 5-fold cross- validation. For comparison, results were also acquired using only pre-operative tilt magnitude and tilt direction as input features. As shown in Table 3, the estimated postoperative tilt magnitude and direction results obtained with the additional features indicated above outperformed the estimation results obtained using only the preoperative tilt direction for estimating the postoperative tilt direction and using only the preoperative tilt magnitude for estimating the postoperative tilt magnitude.

[0079] TABLE 3

[0080] Such improved results may be useful in the creation of pseudophakic eye models and selection of particular IOLS based on estimated tilt magnitude and direction for different IOL models for a particular patient.

[0081] It will be appreciated that variants of the above-disclosed embodiments and other disclosed features and functions, or alternatives thereof, may be combined into many other different systems or applications. Various presently unforeseen or unanticipated alternatives, modifications, variations, or improvements therein may be subsequently made by those skilled in the art which arc also intended to be encompassed by the following claims.

[0082] All publications, patents, and patent applications cited herein are hereby incorporated by reference in their entirety for all purposes.

[0083] Cited references:

[0084] Mori, Y., Yamauchi, T., Tokuda, S. et al. Machine learning adaptation of intraocular lens power calculation for a patient group. Eye and Vis 8, 42 (2021). https: / / doi.org / 10. 1186 / s40662-021-00265-z

[0085] Guo, D., He, W., Wei, L. et al. The Zhu-Lu formula: a machine learning-based intraocular lens power calculation formula for highly myopic eyes. Eye and Vis 10, 26 (2023). https: / / doi.Org / 10.l 186 / s40662 -023-00342-5

[0086] Debellemaniere G, Dubois M, Gauvin M, Wallerstein A, Brenner LF, Rampat R, Saad A, Gatinel D. The PEARL-DGS Formula: The Development of an Open- source Machine Learning-based Thick IOL Calculation Formula. Am J Ophthalmol. 2021 Dec;232:58-69. doi: 10.1016 / j.ajo.2021.05.004. Epub 2021 May 13. PMID: 33992611.

[0087] Tsessler M, Cohen S, Wang L, Koch DD, Zadok D, Abulafia A. Evaluating the prediction accuracy of the Hill-RBF 3.0 formula using a heteroscedastic statistical method. J Cataract Refract Surg. 2022 Jan 1 ;48(l):37-43. doi: 10.1097 / j.jcrs.0000000000000702. PMID: 34016821.

[0088] Sramka M, Slovak M, Tuckova J, Stodulka P. Improving clinical refractive results of cataract surgery by machine learning. PeerJ. 2019 Jul 2;7:e7202. doi: 10.7717 / peerj.7202. PMID: 31304064; PMCTD: PMC661 1496

[0089] Ladas JG, Siddiqui AA, Devgan U, et al. A 3-D "Super Surface" Combining Modern Intraocular Lens Formulas to Generate a "Super Formula" and Maximize Accuracy. JAMA Ophthalmol 2015;133: 1431-6.

[0090] Savini G, Taroni L, Hoffer KJ. Recent developments in intraocular lens power calculation methods-update 2020. Ann Transl Med. 2020 Nov;8(22): 1553. doi: 10.21037 / atm-20-2290. PMID: 33313298; PMCID: PMC7729321.

[0091] Ortiz S, Siedlecki D, Remon L, Marcos S. Optical coherence tomography for quantitative surface topography. Appl Opt. 2009 Dec 10;48(35):6708-15. doi: 10.1364 / AO.48.006708. PMID: 20011011.

[0092] Eduardo Martinez-Enriquez, Susana Marcos; Method of obtaining a complete shape of a crystalline lens from in-vivo measurements taken by optical imaging techniques and method of estimating an intraocular lens position from the complete shape of the crystalline lens in a cataract surgery. US20230274451A1

[0093] Eduardo Martinez-Enriquez, Pablo Perez-Merino, Sonia Duran-Poveda, et al. Estimation of intraocular lens position from full crystalline lens geometry: towards a new generation of intraocular lens power calculation formulas. Sci Rep 8, 9829 (2018). https: / / doi.org / ! 0.1038 / s41598-018-28272-6.

[0094] Eduardo Martinez-Enriquez, Susana Marcos, Carlos Dorronsoro. Method of estimating a full shape of the crystalline lens from measurements taken by optic imaging techniques and method of estimating an intraocular lens position in a cataract surgery. US10810756B2.

[0095] Eduardo Martinez-Enriquez, Mengchan Sun, Miriam Velasco-Ocana, Judith Birkenfeld, Pablo Perez-Merino, Susana Marcos; Optical Coherence Tomography Based Estimates of Crystalline Lens Volume, Equatorial Diameter, and Plane Position. Invest. Ophthalmol. Vis. Sci. 2016;57(9):OCT600-OCT610.

[0096] Eduardo Martinez-Enriquez, Alberto de Castro, and Susana Marcos, "Eigcnlcnscs: a new model for full crystalline lens shape representation and its applications," Biomed. Opt. Express 11, 5633-5649 (2020).

[0097] Carl Edward Rasmussen, Christopher K. I. Williams, “Gaussian Processes for Machine Learning1', The MIT Press, 2005.

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Claims

CLAIMS1. A method of determining a post-operative estimated lens position (ELP) of an intraocular lens (IOL) in an eye of a patient, for use in selecting an IOL for insertion into the eye, comprising the steps of: generating an ELP equation based on a machine learning analysis of a data set including selected parameters defining pre-operative ocular geometric features of a plurality of eyes and post-operative IOL positioning in the plurality of eyes, wherein the selected parameters include at least one parameter based on a full shape of the crystalline lens of the eye; obtaining data defining pre-operative ocular geometric features of an eye of a patient from pre-operative in vivo quantitative optical coherence tomography imaging of the eye; and determining a post-operative ELP for the eye of the patient based on the ELP equation and the data obtained from pre-operative in vivo quantitative optical coherence tomography.

2. The method of claim 1 , wherein the data set employed in the machine learning analysis includes pre-operative 3-dimensional biometric data obtained from quantification of anterior segment OCT including in vivo visible portions of the crystalline lens, and further comprising determining the at least one parameter based on a full shape of the crystalline lens based on at least one eigenlens deformation pattern coefficient relative to an average lens shape obtained from a training set of isolated crystalline lenses.

3. The method of claim 1 , wherein ELP equation is generated further based on where the data set includes at least one IOL type parameter.

4. The method of claim 1 , wherein ELP equation is generated further based on where the data set includes an RAC parameter.

5. The method of claim 1, wherein ELP equation is generated further based on where the data set includes an ALOCT parameter.

6. The method of claim 1, wherein the selected parameters comprise RAC, ALOCT, IOL type, ACD, VCD, CT, LT, RAL 3D, and RPL 3D.

7. The method of claim 1, wherein the selected parameters comprise RAC, ALOCT, IOL type, ACD, VCD, CT, and LT.

8. The method of claim 1, wherein the selected parameters comprise RAC, ALOCT, IOL type, ACD, VCD, CT, LT, RAL 3D, RPL 3D, and DIA eigen lenses.

9. The method of claim 1, wherein the selected parameters comprise RAC, ALOCT, IOL type, ACD, RAL 3D, RPL 3D, and al eigenlens coefficient.

10. The method of claim 1 , wherein the selected parameters comprise ALioLMaster, IOL type, ACD, cl eigencenter coefficient, EPP iovs, Cyl, VOL iovs.

11. The method of any one of claims 1-10, wherein the ELP equation is generated based on a Ridge Regression model.

12. The method of any one of claims 1-10, wherein the ELP equation is generated based on a Gaussian process regression (GPR) model.

13. The method of claim 1, wherein the selected parameters comprise ACD, IOL type, al eigenlens coefficient, and ALOCT.

14. The method of claim 13, wherein the ELP equation is generated based on a Gaussian process regression (GPR) model.

15. The method of any one of claims 1-14, further comprising determining a post-operative estimated lens tilt of the IOL in the eye of the patient, for use with the ELP in selecting an IOL for insertion into the eye, comprising the further steps of: generating an estimated IOL tilt equation based on a machine learning analysis of a data set including selected parameters defining pre-operative ocular geometric features of a plurality of eyes and post-operative IOL tilt in the plurality of eyes; obtaining data defining pre-operative ocular geometric features of an eye of a patient from pre-operative in vivo quantitative optical coherence tomography imaging of the eye; and determining a post-operative estimated IOL tilt for the eye of the patient based on the estimated IOL tilt equation and the data obtained from pre-operative in vivo quantitative optical coherence tomography.

16. The method of claim 15, wherein the selected parameters include at least one parameter based on a full shape of the crystalline lens of the eye.

17. The method of claim 16, wherein the estimated IOL tilt includes estimated tilt direction, and the selected parameters comprise pre-operative tilt direction, pupil size, estimated full crystalline lens size, and pre-operative tilt magnitude.

18. The method of claim 15, wherein the estimated IOL tilt includes estimated tilt magnitude, and the selected parameters comprise pre-operative tilt magnitude, crystalline lens equatorial plane position, pupil size, radius of curvature of anterior cornea, and patient age.

19. A method according to any one of claims 1-18, further comprising selecting an IOL based at least in part on the determined post-operative ELP, and inserting the selected IOL into the eye of the patient.

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