The refractive outcome of cataract surgery is directly related to patient satisfaction and postoperative visual quality, with the accurate calculation of intraocular lens (IOL) power being a central component. Traditional IOL power calculation formulas are based on ocular biometric parameters and classical optical models. While they perform well within the normal axial length range, their predictive accuracy significantly declines in complex ocular conditions such as short eyes, long eyes, and eyes with prior corneal refractive surgery (1). In recent years, artificial intelligence (AI)-based IOL formulas have rapidly emerged, demonstrating superior potential compared to traditional methods and offering new solutions for complex ocular anatomies (2).
Unlike traditional formulas based on statistical regression principles, AI-based IOL calculation formulas can better handle complex non-linear relationships among parameters. AI-based formulas are trained using vast clinical datasets comprising tens of thousands of postoperative cases. The input parameters are also more comprehensive, including not only routine biometric measurements but also multidimensional variables such as patient age, lens thickness, corneal white-to-white distance, and ethnicity. Through algorithms like neural networks, AI can automatically learn and extract complex features and interactions from these high-dimensional data that influence postoperative refractive outcomes.
Currently, AI-based calculation formulas mainly fall into three categories: First, purely data-driven IOL calculation formulas, constructed entirely based on machine learning algorithms, such as the Hill-RBF formula, Karmona formula, and Nallasamy formula (3, 4, 5). Second, IOL calculation formulas that combine optical theory with AI. These formulas build upon traditional optical theory-based formulas and utilize AI to optimize the prediction of key parameters, such as the Kane formula, PEARL-DGS formula, and Hoffer QST formula (6, 7, 8, 9). Third, general optimization algorithms. This approach does not create new formulas but uses AI to integrate multiple existing formulas, selecting the most appropriate one for calculation based on specific ocular parameters. This method can effectively reduce selection bias and improve calculation accuracy (10).
Substantial clinical research has demonstrated that the overall prediction error of the new generation of AI formulas is significantly lower than that of traditional formulas. Darcy et al. (2020) (11) in a study of 10,930 eyes, found that the Kane formula (MAE=0.377,within±0.5D=72.0%) outperformed Hill-RBF2.0 (MAE=0.387, within±0.5D = 71.2%), with both significantly surpassing third- and fourth-generation traditional formulas. Furthermore, AI formulas have shown superior predictive performance in eyes with extremely long axial length (>26.0 mm), extremely short axial length (<22.0mm), and post-corneal refractive surgery eyes.
A study retrospectively analyzed 115 highly myopic patients (12), comparing the predictive accuracy of four traditional formulas and 7 AI-based IOL formulas. The results indicated that most AI formulas were significantly superior to traditional methods in terms of mean absolute error (MAE) and standard deviation (SD). Specifically, Hill-RBF 3.0, PEARL-DGS, and Kane showed significantly lower MAE in the long axial length group (AL≥26mm) compared to the Holladay II formula (P < 0.05), and demonstrated more stable performance across different axial lengths and keratometry ranges. This suggests that the distribution of prediction errors from AI models is more concentrated, significantly reducing the incidence of large refractive errors that lead to severe patient dissatisfaction.
AI-based formulas have profound implications for clinical practice. They significantly enhance the refractive precision of cataract surgery, enabling the formulation of more personalized postoperative refractive targets to meet specific visual needs. When dealing with special ocular conditions such as prior corneal refractive surgery or extreme axial lengths, ophthalmologists can utilize more accurate AI-based formulas, substantially improving refractive prediction performance. Moreover, multi-formula comparison via ensemble algorithms optimizes the clinical decision-making process, assisting surgeons in making more robust choices among numerous formula results.
In the future, the application of artificial intelligence in IOL calculation will continue to deepen. With the continuous expansion of datasets and further optimization of algorithms, predictive accuracy is expected to improve further. Despite existing challenges, there is no doubt that AI-based IOL power calculation formulas are becoming an indispensable component of precise cataract surgery.
Unlike traditional formulas based on statistical regression principles, AI-based IOL calculation formulas can better handle complex non-linear relationships among parameters. AI-based formulas are trained using vast clinical datasets comprising tens of thousands of postoperative cases. The input parameters are also more comprehensive, including not only routine biometric measurements but also multidimensional variables such as patient age, lens thickness, corneal white-to-white distance, and ethnicity. Through algorithms like neural networks, AI can automatically learn and extract complex features and interactions from these high-dimensional data that influence postoperative refractive outcomes.
Currently, AI-based calculation formulas mainly fall into three categories: First, purely data-driven IOL calculation formulas, constructed entirely based on machine learning algorithms, such as the Hill-RBF formula, Karmona formula, and Nallasamy formula (3, 4, 5). Second, IOL calculation formulas that combine optical theory with AI. These formulas build upon traditional optical theory-based formulas and utilize AI to optimize the prediction of key parameters, such as the Kane formula, PEARL-DGS formula, and Hoffer QST formula (6, 7, 8, 9). Third, general optimization algorithms. This approach does not create new formulas but uses AI to integrate multiple existing formulas, selecting the most appropriate one for calculation based on specific ocular parameters. This method can effectively reduce selection bias and improve calculation accuracy (10).
Substantial clinical research has demonstrated that the overall prediction error of the new generation of AI formulas is significantly lower than that of traditional formulas. Darcy et al. (2020) (11) in a study of 10,930 eyes, found that the Kane formula (MAE=0.377,within±0.5D=72.0%) outperformed Hill-RBF2.0 (MAE=0.387, within±0.5D = 71.2%), with both significantly surpassing third- and fourth-generation traditional formulas. Furthermore, AI formulas have shown superior predictive performance in eyes with extremely long axial length (>26.0 mm), extremely short axial length (<22.0mm), and post-corneal refractive surgery eyes.
A study retrospectively analyzed 115 highly myopic patients (12), comparing the predictive accuracy of four traditional formulas and 7 AI-based IOL formulas. The results indicated that most AI formulas were significantly superior to traditional methods in terms of mean absolute error (MAE) and standard deviation (SD). Specifically, Hill-RBF 3.0, PEARL-DGS, and Kane showed significantly lower MAE in the long axial length group (AL≥26mm) compared to the Holladay II formula (P < 0.05), and demonstrated more stable performance across different axial lengths and keratometry ranges. This suggests that the distribution of prediction errors from AI models is more concentrated, significantly reducing the incidence of large refractive errors that lead to severe patient dissatisfaction.
AI-based formulas have profound implications for clinical practice. They significantly enhance the refractive precision of cataract surgery, enabling the formulation of more personalized postoperative refractive targets to meet specific visual needs. When dealing with special ocular conditions such as prior corneal refractive surgery or extreme axial lengths, ophthalmologists can utilize more accurate AI-based formulas, substantially improving refractive prediction performance. Moreover, multi-formula comparison via ensemble algorithms optimizes the clinical decision-making process, assisting surgeons in making more robust choices among numerous formula results.
In the future, the application of artificial intelligence in IOL calculation will continue to deepen. With the continuous expansion of datasets and further optimization of algorithms, predictive accuracy is expected to improve further. Despite existing challenges, there is no doubt that AI-based IOL power calculation formulas are becoming an indispensable component of precise cataract surgery.
References
- X Li et al., “Accuracy of 14 intraocular lens power calculation formulas in extremely long eyes,” Graefes Arch Clin Exp Ophthalmol, 262, 3619 (2024).
- Y Suzuki et al., “Artificial intelligence driven intraocular lens power calculation in extreme axial myopia,” Sci Rep, 15, 36921 (2025).
- M Tsessler et al., “Evaluating the prediction accuracy of the Hill-RBF 3.0 formula using a heteroscedastic statistical method,” J Cataract Refract Surg, 48, 37 (2022). PMID: 34705874.
- D Carmona González, C Palomino Bautista, “Accuracy of a new intraocular lens power calculation method based on artificial intelligence,” Eye (Lond), 35, 517 (2021). PMID: 32760076.
- T Li et al., “Evaluation of the Nallasamy formula: a stacking ensemble machine learning method for refraction prediction in cataract surgery,” Br J Ophthalmol, 107, 1066 (2023). PMID: 35210309.
- BJ Connell, JX Kane, “Comparison of the Kane formula with existing formulas for intraocular lens power selection,” BMJ Open Ophthalmol, 4, e000251 (2019). PMID: 31080852.
- D Gatinel et al., “Determining the Theoretical Effective Lens Position of Thick Intraocular Lenses for Machine Learning-Based IOL Power Calculation and Simulation,” Transl Vis Sci Technol, 10, 27 (2021). PMID: 33859812.
- J Ladas et al., “Improvement of Multiple Generations of Intraocular Lens Calculation Formulae with a Novel Approach Using Artificial Intelligence,” Transl Vis Sci Technol, 10, 7 (2021). PMID: 33796423.
- L Taroni et al., “Comparison of the new Hoffer QST with 4 modern accurate formulas,” J Cataract Refract Surg, 49, 378 (2023). PMID: 36701241.
- Y Suzuki et al., “Artificial intelligence driven intraocular lens power calculation in extreme axial myopia,” Sci Rep, 15, 36921 (2025).
- K Darcy et al., “Assessment of the accuracy of new and updated intraocular lens power calculation formulas in 10 930 eyes from the UK National Health Service,” J Cataract Refract Surg, 46, 2 (2020). PMID: 31743270.
- X Jiang et al., “Comparative evaluation of traditional and AI-based intraocular lens power calculation formulas in highly myopic eyes,” BMC Ophthalmol, 25, 507 (2025).
