Considerations on the Castrop formula for calculation of intraocular lens power

Abstract

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.

Strategies for formula constant optimisation for intraocular lens power calculation

“…A systematic optimisation of formula constants for statistical metrics of the refractive outcome requires more advanced techniques than simple reorganisation of the formula to solve for the formula constant [ 18 ]. In engineering, nonlinear iterative techniques are typically used to derive the best formula constant(s) in terms of minimising any classical statistical metrics of the prediction error.…”

“…For the Haigis formula we used 2 versions: the simplified option (Haigis1) with preset values a1 = 0.4/a2 = 0.1 and customisation of a0, and additionally the option with a customised formula constant triplet a0/a1/a2 (Haigis3) [ 19 ]. For simplicity when using the Castrop formula, instead of using the CCT and the curvature data of the corneal back surface, we replaced CCT by 0.55 mm and the corneal back surface curvature was estimated from the corneal front surface curvature with a fixed anterior to posterior curvature ratio of 0.834 as published by Langenbucher et al [ 18 ], and a sum of segments correction according to Cooke [ 21 , 22 ] was used for the axial length. All formulae included in this analysis were reorganised and solved for the SEQ as a function of preoperative biometrical data and PIOL.…”

“…In addition to these classical calculation concepts, over the last 2 or decades many IOL power calculation strategies such as the Holladay 2, the Barrett, Kane, T2, or DGS formula have been presented, and their relative merits discussed in many scientific reports [ 15 – 17 ]. Only a few of these modern IOL power calculation formulae (for example, the Castrop formula) have been disclosed by the formula authors [ 16 , 18 ]. In contrast to all these formulae, IOL power calculations using deep learning (e.g.…”

“…However, there is in general no consensus on the optimisation technique for formula constants [ 18 – 20 ]. If the IOL power calculation formula is fully disclosed and uses only one formula constant, the formula can be reorganised to solve for the formula constant.…”

“…a0/a1/a2 with the Haigis formula). In IOL calculation concepts with more than one formula constant which do not define the ELP with a multilinear superposition (such as the Castrop formula), optimisation procedures fail, and nonlinear optimisation strategies have to be applied [ 18 ].…”