A vergence-based calculation framework for optimal rotational adjustment of toric supplementary intraocular lenses to minimise residual refractive cylinder.

Abstract

Purpose: To present a transparent, physics-based, and generalisable calculation framework to predict the optimal rotational adjustment of toric supplementary intraocular lenses (SIOLs), comprising toric phakic intraocular lenses implanted in the phakic eye and toric AddOn (secondary sulcus-fixated) lenses implanted in the pseudophakic eye, quantifying the expected refractive benefit across four corneal models.

Methods: A paraxial vergence-based calculation framework was implemented to predict the optimal toric axis of a misaligned SIOL. Required inputs were the measured manifest refraction at spectacle plane, corneal power (using either thin- or thick-cornea models), labelled equivalent and toric power of the SIOL, measured SIOL axis, and axial SIOL position. The effective lens position was estimated by combining the measured back-vertex position with an offset between the back-vertex plane and the image-sided principal plane, derived from legacy phakic lens design data or custom template SIOL models. Forward and backward spherocylindrical vergence transformations were embedded in a nonlinear sequential quadratic programming optimisation to identify the SIOL axis that minimised residual refractive cylinder. The method was demonstrated in four representative clinical scenarios, including phakic, pseudophakic , keratoplasty, and prior laser vision correction eyes.

Results: In all examples, the model predicted a specific rotational adjustment of the SIOL (16-18°) that substantially reduced refractive cylinder. Absolute reductions ranged from 1.7 to 2.4 D, corresponding to relative cylinder reductions of 67-94%. The framework successfully accommodated different corneal models and lens types, and provided predicted postoperative refraction and quantitative performance metrics.

Conclusions: This framework enables individualised planning of toric SIOL realignment across diverse corneal models and lens geometries. Explicitly defining optical assumptions and vergence transformations allows reproducible prediction of both optimal rotation and expected refractive benefit using routine clinical inputs. Prospective clinical validation is warranted.