Formula constant optimisation techniques including variation of keratometer or corneal refractive index and consideration for classical and modern IOL formulae

by Achim Langenbucher, Nóra Szentmáry, Alan Cayless, Jascha Wendelstein, Peter Hoffmann

To investigate whether variation of the keratometer/corneal refractive index nK/nC improves the performance (prediction error PE) of classical and a modern intraocular lens (IOL) power calculation formula and further, to establish whether any trend error of PE for corneal radius R could be eliminated using formula constant and nK/nC optimisation.

Based on 2 large datasets (1: N = 888 Hoya Vivinex aberration-correcting and 2: N = 822 Alcon SA60AT spherical lens) a classical formula constant optimisation has been performed for the Hoffer Q, Holladay 1, Haigis and Castrop formulae, to minimise the root mean squared (rms) PE (situation A). In two further optimisations, the formula constants and the formula specific nK/nC value were optimised to minimise the rms PE (situation B) or rms PE and trend error of PE for R (situation C). Nonlinear iterative optimisation strategy was applied according to Levenberg-Marquardt.

Optimising for rms PE and trend error (C) mainly improved the performance of the Holladay 1. The Haigis formula also showed a slight improvement compared to (A). The Hoffer Q formula shows no relevant trend error of PE for R. In contrast, the Holladay shows a positive and the Haigis (and the Castrop a slight) negative trend error of PE for R. The trend error could be fully eliminated by optimising formula constants and nK/nC in (B), but this was at the cost of overall performance in the case of the Holladay 1 formula.

Classical IOL calculation concepts should be critically examined for potential improvement of formula performance by variation of the empirical nK/nC value defined in the formula. With additional degrees of freedom additional optimisation terms such as trend errors might be considered in new intelligent optimisation strategies.