Abstract
BackgroundTo explain the concept of the Castrop lens power calculation formula and show the application and results from a large dataset compared to classical formulae.MethodsThe 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.ResultsThe 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.ConclusionThe 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.
Highlights
Since the introduction of biometry instruments for measuring axial eye length and publication of the first formulae by Fyodorov in 1967 [1] and by Gernet in 1970 [2], many calculation schemes have been proposed for predicting the power of an artificial lens in cataract surgery
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
Summary
Since the introduction of biometry instruments for measuring axial eye length and publication of the first formulae by Fyodorov in 1967 [1] and by Gernet in 1970 [2], many calculation schemes have been proposed for predicting the power of an artificial lens in cataract surgery. The classical theoretical-optical formulae in use today are the SRKT [4, 5], Hoffer-Q [6,7,8], Holladay1 [9], and the Haigis formula [3] The latter is sometimes used in a simplified form with standard values for constants a1 = 0.4 and a2 = 0.1 and optimization of a0 only, or in a version with triple constant optimization a0/a1/a2 which appears to yield superior results in long and short eyes. Some other calculation strategies are based on full aperture raytracing without simplifications to linear Gaussian optics (e.g. Okulix or PhakoOptics) or on artificial intelligence (e.g. Hill RBF calculator or PEARL formula), where a large dataset replaces an anatomical or optical model [10] All of these concepts claim to yield superior results to other formulae. 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
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