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Updated: Jun 30, 2025

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Surrogate optimisation strategies for intraocular lens formula constant optimisation.

Achim Langenbucher1, Jascha Wendelstein1,2, Alan Cayless3

  • 1Department of Experimental Ophthalmology, Saarland University, Homburg/Saar, Germany.

Acta Ophthalmologica
|March 20, 2024
PubMed
Summary

Surrogate optimization (SO) effectively optimizes intraocular lens formula constants for improved accuracy in cataract surgery. This data-driven method offers a powerful alternative to traditional algorithms for precise refractive outcomes.

Keywords:
formula constant optimisationformula prediction errorlens power calculationnonlinear iterative algorithmperformance metricssurrogate optimisation

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Area of Science:

  • Ophthalmology
  • Biomedical Engineering
  • Computational Science

Background:

  • Accurate intraocular lens (IOL) power calculation is crucial for successful cataract surgery outcomes.
  • Traditional methods for optimizing IOL formula constants can be complex and may not always yield optimal results.

Purpose of the Study:

  • To evaluate surrogate optimization (SO) as a data-driven, nonlinear adaptive iterative strategy for optimizing IOL formula constants.
  • To compare the performance of SO against the established Levenberg-Marquardt algorithm.

Main Methods:

  • Implemented a SO algorithm to minimize root mean squared prediction error (rmsPE) for SRKT, Hoffer Q, Holladay, Haigis, and Castrop formulas.
  • Utilized a Gaussian Process estimator and restricted SO iterations (200 or 700) in a dataset of 888 eyes implanted with Hoya Vivinex IOLs.

Main Results:

  • SO demonstrated stable convergence in fewer than 150 iterations across all tested formulas.
  • Achieved systematic reduction in rmsPE, reaching as low as 0.3449 diopters.
  • Optimized constants for each formula matched previously reported values.

Conclusions:

  • Surrogate optimization is a powerful, adaptive nonlinear algorithm for optimizing IOL formula constants.
  • SO is gradient-independent and capable of navigating complex parameter spaces with multiple local minima.
  • This method offers a robust, data-driven approach for enhancing IOL power calculation accuracy.