Limitations of constant optimization with disclosed intraocular lens power formulae

Langenbucher, Achim; Hoffmann, Peter; Cayless, Alan; Wendelstein, Jascha and Szentmáry, Nóra (2023). Limitations of constant optimization with disclosed intraocular lens power formulae. Journal of Cataract and Refractive Surgery (Early Access).



Purpose: Investigating impact of formula constants on predicted refraction and limitations of constant optimization for classical and modern intraocular lens (IOL) power calculation formulae.
Setting: Tertiary Care Center.
Design: Retrospective single centre consecutive case series.
Methods: Analysis based on a dataset of 888 eyes before and after cataract surgery with IOL implantation (Hoya Vivinex). Spherical equivalent refraction predSEQ was predicted using IOLMaster 700 (IOLM) data, IOL power, and formula constants from IOLCon ( The formula prediction error (PE) was derived as predSEQ minus achieved spherical equivalent refraction for the SRKT, Hoffer Q, Holladay, Haigis, and Castrop formulae. The gradient of predSEQ (gradSEQ) as a measure for the impact of the constant on refraction was calculated and used for constant optimization. Results: using initial formula constants the mean PE was -0.1782±0.4450/-0.1814±0.4159/-0.1702±0.4207/-0.1211±0.3740/-0.1912±0.3449 dpt for the SRKT/Hoffer Q/Holladay/Haigis/Castrop formula. All gradSEQ (except gradSEQ for the Castrop R) decay with axial length because of interaction with the effective lens position (ELP). Constant optimization for a zero mean PE (SD: 0.4410/0.4307/0.4272/0.3742/0.3436 dpt) results in a change in the PE trend over axial length in all formulae where the constant acts directly on the ELP.
Conclusion: With IOL power calculation formulae where the constant(s) act directly on the ELP, a change in the constant(s) always changes the trend of the PE according to gradSEQ. Formulae where at least one constant does not act on the ELP have more flexibility to zero the mean or median PE without coupling to a PE trend error over axial length.

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