Considerations on the Castrop formula for calculation of intraocular lens power

Achiron, Asaf; Langenbucher, Achim; Szentmáry, Nóra; Cayless, Alan; Weisensee, Johannes; Fabian, Ekkehard; Wendelstein, Jascha and Hoffmann, Peter (2021). Considerations on the Castrop formula for calculation of intraocular lens power. PLOS ONE, 16(6) e0252102.



Background: To explain the concept of the Castrop lens power calculation formula and show the application and results from a large dataset compared to classical formulae.

Methods: The Castrop vergence formula is based on a pseudophakic model eye with 4 refractive surfaces. This was compared against the SRKT, Hoffer-Q, Holladay1, simplified Haigis with 1 optimized constant and Haigis formula with 3 optimized constants. A large dataset of preoperative biometric values, lens power data and postoperative refraction data was split into training and test sets. The training data were used for formula constant optimization, and the test data for cross-validation. Constant optimization was performed for all formulae using nonlinear optimization, minimising root mean squared prediction error.

Results: The constants for all formulae were derived with the Levenberg-Marquardt algorithm. Applying these constants to the test data, the Castrop formula showed a slightly better performance compared to the classical formulae in terms of prediction error and absolute prediction error. Using the Castrop formula, the standard deviation of the prediction error was lowest at 0.45 dpt, and 95% of all eyes in the test data were within the limit of 0.9 dpt of prediction error.

Conclusion: The calculation concept of the Castrop formula and one potential option for optimization of the 3 Castrop formula constants (C, H, and R) are presented. In a large dataset of 1452 data points the performance of the Castrop formula was slightly superior to the respective results of the classical formulae such as SRKT, Hoffer-Q, Holladay1 or Haigis.

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