Using Artificial Intelligence and Novel Polynomials to Predict Subjective Refraction

Optimizing Refractive Outcomes of SMILE: Artificial Intelligence versus Conventional State-of-the-Art Nomograms

PURPOSE

AI (artificial intelligence)-based methodologies have become established tools for researchers and physicians in the entire field of ophthalmology. However, the potential of AI to optimize the refractive outcome of keratorefractive surgery by means of machine learning (ML)-based nomograms has not been exhausted yet. In this study, we wanted to comprehensively compare state-of-the-art conventional nomograms for Small-Incision-Lenticule-Extraction (SMILE) with a novel ML-based nomogram regarding both their spherical and astigmatic predictability.

METHODS

A total of 1,342 eyes were analyzed for creation of three different nomograms based on a linear model (LM), a generalized additive mixed model (GAMM) and an artificial-neuronal-network (ANN), respectively. A total of 16 patient- and treatment-related features were included. Each model was trained by 895 eyes and validated by the remaining 447 eyes. Predictability was assessed by the difference between attempted and achieved change in spherical equivalent (SE) and the difference between target induced astigmatism (TIA) and surgically induced astigmatism (SIA). The root mean squared error (RMSE) of each model was computed as a measure of overall model performance.

RESULTS

The RMSE of LM, GAMM and ANN were 0.355, 0.348 and 0.367 for the prediction of SE and 0.279, 0.278 and 0.290 for the astigmatic correction, respectively. By applying the created models, the theoretical yield of eyes within ±0.50 D of SE from target refraction improved from 82 to 83% (LM), 84% (GAMM) and 83% (ANN), respectively. Astigmatic outcomes showed an improvement of eyes within ±0.50 D from TIA from 90 to 93% (LM), 93% (GAMM) and 92% (ANN), respectively. Subjective manifest refraction was the single most influential covariate in all models.

CONCLUSION

Machine learning endorsed the validity of state-of-the-art linear and non-linear SMILE nomograms. However, improving the accuracy of subjective manifest refraction seems warranted for optimizing ±0.50 D SE predictability beyond an apparent methodological 90% limit.

Insights into artificial intelligence in myopia management: from a data perspective

Given the high incidence and prevalence of myopia, the current healthcare system is struggling to handle the task of myopia management, which is worsened by home quarantine during the ongoing COVID-19 pandemic. The utilization of artificial intelligence (AI) in ophthalmology is thriving, yet not enough in myopia. AI can serve as a solution for the myopia pandemic, with application potential in early identification, risk stratification, progression prediction, and timely intervention. The datasets used for developing AI models are the foundation and determine the upper limit of performance. Data generated from clinical practice in managing myopia can be categorized into clinical data and imaging data, and different AI methods can be used for analysis. In this review, we comprehensively review the current application status of AI in myopia with an emphasis on data modalities used for developing AI models. We propose that establishing large public datasets with high quality, enhancing the model's capability of handling multimodal input, and exploring novel data modalities could be of great significance for the further application of AI for myopia.

Machine Learning Models for Predicting Long-Term Visual Acuity in Highly Myopic Eyes

Importance

High myopia is a global concern due to its escalating prevalence and the potential risk of severe visual impairment caused by pathologic myopia. Using artificial intelligence to estimate future visual acuity (VA) could help clinicians to identify and monitor patients with a high risk of vision reduction in advance.

Objective

To develop machine learning models to predict VA at 3 and 5 years in patients with high myopia.

Design, Setting, and Participants

This retrospective, single-center, cohort study was performed on patients whose best-corrected VA (BCVA) at 3 and 5 years was known. The ophthalmic examinations of these patients were performed between October 2011 and May 2021. Thirty-four variables, including general information, basic ophthalmic information, and categories of myopic maculopathy based on fundus and optical coherence tomography images, were collected from the medical records for analysis.

Main Outcomes and Measures

Regression models were developed to predict BCVA at 3 and 5 years, and a binary classification model was developed to predict the risk of developing visual impairment at 5 years. The performance of models was evaluated by discrimination metrics, calibration belts, and decision curve analysis. The importance of relative variables was assessed by explainable artificial intelligence techniques.

Results

A total of 1616 eyes from 967 patients (mean [SD] age, 58.5 [14.0] years; 678 female [70.1%]) were included in this analysis. Findings showed that support vector machines presented the best prediction of BCVA at 3 years (R2 = 0.682; 95% CI, 0.625-0.733) and random forest at 5 years (R2 = 0.660; 95% CI, 0.604-0.710). To predict the risk of visual impairment at 5 years, logistic regression presented the best performance (area under the receiver operating characteristic curve = 0.870; 95% CI, 0.816-0.912). The baseline BCVA (logMAR odds ratio [OR], 0.298; 95% CI, 0.235-0.378; P < .001), prior myopic macular neovascularization (OR, 3.290; 95% CI, 2.209-4.899; P < .001), age (OR, 1.578; 95% CI, 1.227-2.028; P < .001), and category 4 myopic maculopathy (OR, 4.899; 95% CI, 1.431-16.769; P = .01) were the 4 most important predicting variables and associated with increased risk of visual impairment at 5 years.

Conclusions and Relevance

Study results suggest that developing models for accurate prediction of the long-term VA for highly myopic eyes based on clinical and imaging information is feasible. Such models could be used for the clinical assessments of future visual acuity.

Prediction of refractive error and its progression: a machine learning-based algorithm

OBJECTIVE

Myopia is the refractive error that shows the highest prevalence for younger ages in Southeast Asia and its projection over the next decades indicates that this situation will worsen. Nowadays, several management solutions are being applied to help fight its onset and development, nonetheless, the applications of these techniques depend on a clear and reliable assessment of risk to develop myopia.

METHODS AND ANALYSIS

In this study, population-based data of Chinese children were used to develop a machine learning-based algorithm that enables the risk assessment of myopia's onset and development. Cross-sectional data of 12 780 kids together with longitudinal data of 226 kids containing age, gender, biometry and refractive parameters were used for the development of the models.

RESULTS

A combination of support vector regression and Gaussian process regression resulted in the best performing algorithm. The Pearson correlation coefficient between prediction and measured data was 0.77, whereas the bias was -0.05 D and the limits of agreement was 0.85 D (95% CI: -0.91 to 0.80D).

DISCUSSION

The developed algorithm uses accessible inputs to provide an estimate of refractive development and may serve as guide for the eye care professional to help determine the individual best strategy for management of myopia.

Objective method for visual performance prediction

We propose, implement, and validate a new objective method for predicting the trends of visual acuity through-focus curves provided by specific optical elements. The proposed method utilized imaging of sinusoidal gratings provided by the optical elements and the definition of acuity. A custom-made monocular visual simulator equipped with active optics was used to implement the objective method and to validate it via subjective measurements. Visual acuity measurements were obtained monocularly from a set of six subjects with paralyzed accommodation for a naked eye and then that eye compensated by four multifocal optical elements. The objective methodology successfully predicts the trends of the visual acuity through-focus curve for all considered cases. The Pearson correlation coefficient was 0.878 for all tested optical elements, which agrees with results obtained by similar works. The proposed method constitutes an easy and direct alternative technique for the objective testing of optical elements for ophthalmic and optometric applications, which can be implemented before invasive, demanding, or costly procedures on real subjects.

Novel Uses and Challenges of Artificial Intelligence in Diagnosing and Managing Eyes with High Myopia and Pathologic Myopia

Myopia is a global health issue, and the prevalence of high myopia has increased significantly in the past five to six decades. The high incidence of myopia and its vision-threatening course emphasize the need for automated methods to screen for high myopia and its serious form, named pathologic myopia (PM). Artificial intelligence (AI)-based applications have been extensively applied in medicine, and these applications have focused on analyzing ophthalmic images to diagnose the disease and to determine prognosis from these images. However, unlike diseases that mainly show pathologic changes in the fundus, high myopia and PM generate even more data because both the ophthalmic information and morphological changes in the retina and choroid need to be analyzed. In this review, we present how AI techniques have been used to diagnose and manage high myopia, PM, and other ocular diseases and discuss the current capacity of AI in assisting in preventing high myopia.

Myopia prediction: a systematic review

Myopia is a leading cause of visual impairment and has raised significant international concern in recent decades with rapidly increasing prevalence and incidence worldwide. Accurate prediction of future myopia risk could help identify high-risk children for early targeted intervention to delay myopia onset or slow myopia progression. Researchers have built and assessed various myopia prediction models based on different datasets, including baseline refraction or biometric data, lifestyle data, genetic data, and data integration. Here, we summarize all related work published in the past 30 years and provide a comprehensive review of myopia prediction methods, datasets, and performance, which could serve as a useful reference and valuable guideline for future research.

Prediction of manifest refraction using machine learning ensemble models on wavefront aberrometry data

PURPOSE

To assess the performance of machine learning (ML) ensemble models for predicting patient subjective refraction (SR) using demographic factors, wavefront aberrometry data, and measurement quality related metrics taken with a low-cost portable autorefractor.

METHODS

Four ensemble models were evaluated for predicting individual power vectors (M, J0, and J45) corresponding to the eyeglass prescription of each patient. Those models were random forest regressor (RF), gradient boosting regressor (GB), extreme gradient boosting regressor (XGB), and a custom assembly model (ASB) that averages the first three models. Algorithms were trained on a dataset of 1244 samples and the predictive power was evaluated with 518 unseen samples. Variables used for the prediction were age, gender, Zernike coefficients up to 5th order, and pupil related metrics provided by the autorefractor. Agreement with SR was measured using Bland-Altman analysis, overall prediction error, and percentage of agreement between the ML predictions and subjective refractions for different thresholds (0.25 D, 0.5 D).

RESULTS

All models considerably outperformed the predictions from the autorefractor, while ASB obtained the best results. The accuracy of the predictions for each individual power vector component was substantially improved resulting in a ± 0.63 D, ±0.14D, and ±0.08 D reduction in the 95% limits of agreement of the error distribution for M, J0, and J45, respectively. The wavefront-aberrometry related variables had the biggest impact on the prediction, while demographic and measurement quality-related features showed a heterogeneous but consistent predictive value.

CONCLUSIONS

These results suggest that ML is effective for improving precision in predicting patient's SR from objective measurements taken with a low-cost portable device.

Prediction of Subjective Refraction From Anterior Corneal Surface, Eye Lengths, and Age Using Machine Learning Algorithms

Purpose

To develop a machine learning regression model of subjective refractive prescription from minimum ocular biometry and corneal topography features.

Methods

Anterior corneal surface parameters (Zernike coefficients and keratometry), axial length, anterior chamber depth, and age were posed as features to predict subjective refractions. Measurements from 355 eyes were split into training (75%) and test (25%) sets. Different machine learning regression algorithms were trained by 10-fold cross-validation, optimized, and tested. A neighborhood component analysis provided features’ normalized weights in predictions.

Results

Gaussian process regression algorithms provided the best models with mean absolute errors of around 1.00 diopters (D) in the spherical component and 0.15 D in the astigmatic components.

Conclusions

The normalized weights showed that subjective refraction can be predicted by only keratometry, age, and axial length. Increasing the topographic description detail of the anterior corneal surface implied by a high-order Zernike decomposition versus adjustment to a spherocylindrical surface is not reflected as improved subjective refraction prediction, which is poor, mainly in the spherical component. However, the highest achievable accuracy differs by only 0.75 D from that of other works with a more exhaustive eye refractive elements description. Although the chosen parameters may have not been the most efficient, applying machine learning and big data to predict subjective refraction can be risky and impractical when evaluating a particular subject at statistical extremes.

Translational Relevance

This work evaluates subjective refraction prediction by machine learning from the anterior corneal surface and ocular biometry. It shows the minimum biometric information required and the highest achievable accuracy.

RESUMEN

Objetivo

El desarrollo de un modelo de regresión de aprendizaje automático prescripción refractiva subjetiva a partir de las características mínimas de la biometría ocular y la superficie corneal.

Métodos

Los parámetros de la superficie corneal anterior (coeficientes de Zernike y queratometría), además de longitudes axiales y de cámara anterior, edades y las refracciones subjetivas no ciclopléjicas de 355 ojos se dividieron en un conjunto de entrenamiento (75%) y otro de test (25%) y se entrenaron diferentes algoritmos de regresión de aprendizaje automático mediante validación cruzada 10 veces, se optimizaron y se probaron sobre el conjunto test.

Resultados

Los algoritmos de regresión del proceso gaussiano proporcionaron los mejores modelos con un error absoluto medio fue de alrededor de 1.00 D en el componente esférico y de 0.25 D en los componentes astigmáticos.

Conclusiones

Los pesos normalizados mostraron que la refracción subjetiva puede predecirse utilizando únicamente la queratometría, la edad y la longitud axial como características. El aumento del detalle de la descripción topográfica de la superficie corneal anterior que supone una descomposición de Zernike de alto orden frente al ajuste a una superficie esferocilíndrica realizado por queratometría no se refleja en una mejora de la predicción de la refracción subjetiva, que es pobre, en cualquier caso, principalmente en el componente esférico. Sin embargo, la máxima precisión alcanzada difiere en sólo 0,75 D de la de otros trabajos con una descripción más exhaustiva de los elementos refractivos del ojo. De todos modos, el aprendizaje automático y los datos masivos aplicados a la predicción de la refracción subjetiva pueden ser arriesgados y poco prácticos cuando se evalúa a un sujeto concreto en los extremos estadísticos, aunque los parámetros elegidos puedan no haber sido los más ineficaces.

Relevancia Traslativa

El trabajo evalúa la predicción de la refracción subjetiva mediante aprendizaje automático a partir de la superficie corneal anterior y la biometría ocular, mostrando la mínima información biométrica requerida y la máxima precisión alcanzable.

Dioptric power and refractive behaviour: a review of methods and applications

Myopia is a global healthcare concern and effective analyses of dioptric power are important in evaluating potential treatments involving surgery, orthokeratology, drugs such as low-dose (0.05%) atropine and gene therapy. This paper considers issues of concern when analysing refractive state such as data normality, transformations, outliers and anisometropia. A brief review of methods for analysing and representing dioptric power is included but the emphasis is on the optimal approach to understanding refractive state (and its variation) in addressing pertinent clinical and research questions.

Although there have been significant improvements in the analysis of refractive state, areas for critical consideration remain and the use of power matrices as opposed to power vectors is one such area. Another is effective identification of outliers in refractive data. The type of multivariate distribution present with samples of dioptric power is often not considered. Similarly, transformations of samples (of dioptric power) towards normality and the effects of such transformations are not thoroughly explored. These areas (outliers, normality and transformations) need further investigation for greater efficacy and proper inferences regarding refractive error. Although power vectors are better known, power matrices are accentuated herein due to potential advantages for statistical analyses of dioptric power such as greater simplicity, completeness, and improved facility for quantitative and graphical representation of refractive state.

Predicting subjective refraction with dynamic retinal image quality analysis

The aim of this work is to evaluate the performance of a novel algorithm that combines dynamic wavefront aberrometry data and descriptors of the retinal image quality from objective autorefractor measurements to predict subjective refraction. We conducted a retrospective study of the prediction accuracy and precision of the novel algorithm compared to standard search-based retinal image quality optimization algorithms. Dynamic measurements from 34 adult patients were taken with a handheld wavefront autorefractor and static data was obtained with a high-end desktop wavefront aberrometer. The search-based algorithms did not significantly improve the results of the desktop system, while the dynamic approach was able to simultaneously reduce the standard deviation (up to a 15% for reduction of spherical equivalent power) and the mean bias error of the predictions (up to 80% reduction of spherical equivalent power) for the handheld aberrometer. These results suggest that dynamic retinal image analysis can substantially improve the accuracy and precision of the portable wavefront autorefractor relative to subjective refraction.

Artificial intelligence in myopia: current and future trends

PURPOSE OF REVIEW

Myopia is one of the leading causes of visual impairment, with a projected increase in prevalence globally. One potential approach to address myopia and its complications is early detection and treatment. However, current healthcare systems may not be able to cope with the growing burden. Digital technological solutions such as artificial intelligence (AI) have emerged as a potential adjunct for myopia management.

RECENT FINDINGS

There are currently four significant domains of AI in myopia, including machine learning (ML), deep learning (DL), genetics and natural language processing (NLP). ML has been demonstrated to be a useful adjunctive for myopia prediction and biometry for cataract surgery in highly myopic individuals. DL techniques, particularly convoluted neural networks, have been applied to various image-related diagnostic and predictive solutions. Applications of AI in genomics and NLP appear to be at a nascent stage.

SUMMARY

Current AI research is mainly focused on disease classification and prediction in myopia. Through greater collaborative research, we envision AI will play an increasingly critical role in big data analysis by aggregating a greater variety of parameters including genomics and environmental factors. This may enable the development of generalizable adjunctive DL systems that could help realize predictive and individualized precision medicine for myopic patients.

Artificial Intelligence in Cornea, Refractive Surgery, and Cataract: Basic Principles, Clinical Applications, and Future Directions

ABSTRACT

Corneal diseases, uncorrected refractive errors, and cataract represent the major causes of blindness globally. The number of refractive surgeries, either cornea- or lens-based, is also on the rise as the demand for perfect vision continues to increase. With the recent advancement and potential promises of artificial intelligence (AI) technologies demonstrated in the realm of ophthalmology, particularly retinal diseases and glaucoma, AI researchers and clinicians are now channeling their focus toward the less explored ophthalmic areas related to the anterior segment of the eye. Conditions that rely on anterior segment imaging modalities, including slit-lamp photography, anterior segment optical coherence tomography, corneal tomography, in vivo confocal microscopy and/or optical biometers, are the most commonly explored areas. These include infectious keratitis, keratoconus, corneal grafts, ocular surface pathologies, preoperative screening before refractive surgery, intraocular lens calculation, and automated refraction, among others. In this review, we aimed to provide a comprehensive update on the utilization of AI in anterior segment diseases, with particular emphasis on the recent advancement in the past few years. In addition, we demystify some of the basic principles and terminologies related to AI, particularly machine learning and deep learning, to help improve the understanding, research and clinical implementation of these AI technologies among the ophthalmologists and vision scientists. As we march toward the era of digital health, guidelines such as CONSORT-AI, SPIRIT-AI, and STARD-AI will play crucial roles in guiding and standardizing the conduct and reporting of AI-related trials, ultimately promoting their potential for clinical translation.

Comparison of Low Degree/High Degree and Zernike Expansions for Evaluating Simulation Outcomes After Customized Aspheric Laser Corrections

Purpose

The purpose of this study was to compare the low degree/high degree (LD/HD) and Zernike Expansion simulation outcomes evaluating the corneal wavefront changes after theoretical conventional and customized aspheric photorefractive ablations.

Methods

Initial anterior corneal surface profiles were modeled as conic sections with pre-operative apical curvature, R0, and asphericity, Q0. Postoperative apical curvature, R1, was computed from intended defocus correction, D, diameter zone, S, and target postoperative asphericity, Q1. Coefficients of both Zernike and LD/HD polynomial expansions of the rotationally symmetrical corneal profile were computed using scalar products. We modeled different values of D, R0, Q0, S, and ΔQ = Q1 to Q0. The corresponding postoperative changes in defocus (Δz20 vs. Δg20), fourth order (Δz40 vs. Δg40) and sixth order (Δz60 vs. Δg60) Zernike and LD/HD spherical aberrations (SAs) were compared. In addition, retrospective clinical data and wavefront measurements were obtained from two examples of two patient eyes before and after corneal laser photoablation.

Results

The z20, varied with both R0 and Q0, whereas the LD/HD defocus coefficient, g20, was relatively robust to changes in asphericity. Variations of apical curvature better correlated with defocus and ΔQ with SA coefficients in the LD/HD classification. The impact of ΔQ was null on g20 but induced significant linear variations in z20 and fourth order SA coefficients. LD/HD coefficients provided a good correlation with the visual performances of the operated eyes.

Conclusions

Simulated variations in postoperative corneal profile and wavefront expansion using the LD/HD approach showed good correlations between defocus and asphericity variations with variations in corneal curvature and SA coefficients, respectively.

Translational Relevance

The relevance of this study was to provide a clinically relevant alternative to Zernike polynomials for the interpretation of wavefront changes after customized aspheric corrections.

The complex relationship between female age and embryo euploidy

BACKGROUND

Female age is the strongest predictor of embryo chromosomal abnormalities and has a nonlinear relationship with the blastocyst euploidy rate: with advancing age there is an acceleration in the reduction of blastocyst euploidy. Aneuploidy was found to significantly increase with maternal age from 30% in embryos from young women to 70% in women older than 40 years old. The association seems mainly due to chromosomal abnormalities occurring in the oocyte. We aimed to elaborate a model for the blastocyst euploid rate for patients undergoing in-vitro fertilization/intra cytoplasmic sperm injection (IVF/ICSI) cycles using advanced machine learning techniques.

METHODS

This was a retrospective analysis of IVF/ICSI cycles performed from 2014 to 2016. In total, data of 3879 blastocysts were collected for the analysis. Patients underwent PGT-Aneuploidy analysis (PGT-A) at the Center for Reproductive Medicine of European Hospital (Rome, Italy) have been included in the analysis. The method involved whole-genome amplification followed by array comparative genome hybridization. To model the rate of euploid blastocysts, the data were split into a train set (used to fit and calibrate the models) and a test set (used to assess models' predictive performance). Three different models were calibrated: a classical linear regression; a gradient boosted tree (GBT) machine learning model; a model belonging to the generalized additive models (GAM).

RESULTS

The present study confirms that female age, which is the strongest predictor of embryo chromosomal abnormalities, and blastocyst euploidy rate have a nonlinear relationship, well depicted by the GBT and the GAM models. According to this model, the rate of reduction in the percentage of euploid blastocysts increases with age: the yearly relative variation is -10% at the age of 37 and -30% at the age of 45. Other factors including male age, female and male Body Mass Index, fertilization rate and ovarian reserve may only marginally impact on embryo euploidy rate.

CONCLUSIONS

Female age is the strongest predictor of embryo chromosomal abnormalities and has a non-linear relationship with the blastocyst euploidy rate. Other factors related to both the male and female subjects may only minimally affect this outcome.

Evaluation of the Performance of Algorithm-Based Methods for Subjective Refraction

Objective: To evaluate the performance of two subjective refraction measurement algorithms by comparing the refraction values, visual acuity, and the time taken by the algorithms with the standard subjective refraction (SSR). Methods: The SSR and two semi-automated algorithm-based subjective refraction (SR1 and SR2) in-built in the Vision-R 800 phoropter were performed in 68 subjects. In SR1 and SR2, the subject’s responses were recorded in the algorithm which continuously modified the spherical and cylindrical component accordingly. The main difference between SR1 and SR2 is the use of an initial fogging step in SR1. Results: The average difference and agreement limits intervals in the spherical equivalent between each refraction method were smaller than 0.25 D, and 2.00 D, respectively. For the cylindrical components, the average difference was almost zero and the agreement limits interval was less than 0.50 D. The visual acuities were not significantly different among the methods. The times taken for SR1 and SR2 were significantly shorter, and SR2 was on average was three times faster than SSR. Conclusions: The refraction values and the visual acuity obtained with the standard subjective refraction and algorithm-based methods were similar on average. The algorithm-based methods were significantly faster than the standard method.

Wavefront sensing, novel lower degree/higher degree polynomial decomposition and its recent clinical applications: A review

We are in the midst of a shift towards using novel polynomials to decompose wavefront aberrations in a more ophthalmologically relevant way. Zernike polynomials have useful mathematical properties but fail to provide clinically relevant wavefront interpretation and predictions. We compared the distribution of the eye's aberrations and demonstrate some clinical applications of this using case studies comparing the results produced by the Zernike decomposition and evaluating them against the lower degree/higher degree (LD/HD) polynomial decomposition basis which clearly dissociates the higher and lower aberrations. In addition, innovative applications validate the LD/HD polynomial basis. Absence of artificial reduction of some higher order aberrations coefficients lead to a more realistic analysis. Here we summarize how wavefront analysis has evolved and demonstrate some of its new clinical applications.