The Evolution of Intraocular Lens Power Calculation Formulas

Shruti Senthilkumar

Introduction

Five generations of IOL power calculation formulas trace a progression from empirical regression to data-driven prediction. Accurate prediction of the effective lens position (ELP), the postoperative anterior-posterior location of the implanted IOL, remains the central, persistent technical challenge (1).

First and Second Generations: Early Theoretical and Regression-Based Models

Modern IOL calculation evolved from early theoretical optics models before empirical regression approaches gained prominence. Binkhorst, Fyodorov, and Galin described optically grounded formulas in the mid-1970s (2,3). The SRK formula correlated axial length (AL) and keratometry (K) empirically with implanted power but performed poorly in atypical eyes due to inadequate ELP prediction (4). SRK II refined this by adjusting the lens constant according to AL,(5) yet limitations in modelling the biometry-ELP relationship persisted.

Third Generation: Paraxial Vergence Formulas

The Hoffer Q, Holladay 1, and SRK/T formulas combined paraxial vergence optics with empirically optimised regression elements (6-8). The SRK/T performed better in long eyes and the Hoffer Q in short eyes,(6,8) a pattern illustrating that no single formula dominates across all biometric subgroups. Holladay introduced the surgeon factor, acknowledging that postoperative lens position partly reflects surgical technique (7). Lens constant optimisation using validated databases such as IOLCon remains essential on top of formula sophistication (9).

Fourth Generation: Multi-Variable and Ray-Tracing Approaches

The Holladay 2 incorporated seven biometric variables (axial length, keratometry, anterior chamber depth, white-to-white corneal diameter, lens thickness, preoperative refraction, and age). to improve ELP modelling (10). The Haigis formula applied a three-constant approach decoupling ELP prediction from keratometry, improving performance particularly in highly myopic and post-refractive eyes (11,12). Olsen introduced the C-constant to relate preoperative crystalline lens anatomy to postoperative IOL position within a ray-tracing-assisted thick-lens framework (13). These advances coincided with optical biometry replacing ultrasonography, reducing systematic measurement error (11). Total keratometry incorporating measured posterior corneal data has become an important adjunct, particularly in post-refractive eyes and toric IOL planning, though postoperative hyperopic error remains problematic (14,15).

Fifth Generation: Advanced Hybrid and AI-Based Systems

The Barrett Universal II applies a Gaussian optics framework with a thick-lens model accounting for principal plane shifts with varying IOL powers, achieving consistent accuracy across diverse biometric ranges (16). Hill-RBF employs a radial basis function neural network for pattern recognition and data interpolation, with accuracy supported by comparative validation across a wide range of axial lengths (17). The Kane formula integrates theoretical optics, regression, and AI components, incorporating lens thickness and central corneal thickness as optional inputs, and has demonstrated high accuracy across large studies (18,19). Pearl-DGS predicts ELP using a machine learning model trained on postoperative outcomes, while EVO achieves this through a thick-lens vergence framework incorporating an individually derived emmetropia factor (20,21). The Ladas Super Formula synthesises multiple established formulas into a three-dimensional surface, selecting the optimal prediction per eye (22). Algorithmic opacity and proprietary training methodologies limit interpretability across several modern formulas, and prospective validation in independent datasets remains mandatory before clinical adoption (23).

Looking Ahead

Future systems will likely integrate personalised dynamic eye models, cloud-based adaptive learning, and automated constant optimisation. The most immediately actionable priorities are wider use of posterior corneal data, improved performance in post-refractive and keratoconic eyes, and greater transparency in AI formula validation methodologies.

References

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