PPubMed24 Feb 2023Cited 13×

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

Achim Langenbucher, Nóra Szentmáry, Alan Cayless, Jascha Wendelstein, Peter Hoffmann, Andrzej Grzybowski

Abstract

In this study for both datasets four situations have been considered for our formula constant optimisation: 1. A standard optimisation of the formula using the keratometer index or corneal refractive index as proposed by the formula authors. The formula constants pACD, SF, a0/a1/a2 and C/H/R were optimised for the Hoffer Q, Holladay 1, Haigis, and Castrop formula to minimise the sum of squared formula prediction error PE. 2. A formula constant optimisation where the formula constants were optimised together with the keratometer index (Hoffer Q, Holladay 1 and Haigis formula) or the corneal ref

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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.

What’s new

i.Performed classical formula constant optimisation for Hoffer Q, Holladay 1, Haigis and Castrop to minimise rms prediction error.
ii.Optimised both formula constants and the formula‑specific keratometer/corneal refractive index (nK/nC) to reduce prediction error and trend error.
iii.Cross‑validated the optimal nK/nC values by applying indices derived from one dataset to the other.

How they did it

The authors retrospectively analysed two large cataract surgery datasets (888 eyes with Hoya Vivinex lenses and 822 eyes with Alcon SA60AT lenses) and applied a Levenberg‑Marquardt nonlinear iterative optimisation to adjust formula constants and nK/nC under three optimisation situations (A‑classical, B‑constants + nK/nC, C‑constants + nK/nC + trend error) and a cross‑validation situation (D).

What they found

Dataset 1 contained 888 eyes and Dataset 2 contained 822 eyes.
Optimising for rms PE and trend error (situation C) mainly improved the Holladay 1 formula performance, with a slight improvement for the Haigis formula.
The trend error of prediction error could be fully eliminated by optimising formula constants and nK/nC (situation B), but this reduced overall performance for the Holladay 1 formula.
Levenberg‑Marquardt optimisation converged in 12–192 iterations (86–311 function evaluations) for all situations.

Caveats

✕Only two datasets with specific hydrophobic acrylic lens designs were examined.
✕Optimisation targeted only the sum of squared prediction error, not other possible metrics.
✕Only the main part of the formulas was modified; the ELP/ALP prediction component remained unchanged.
✕Potential trend error related to axial length was not considered.

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