Calculation of Equivalent and Toric Power in AddOn Lenses Based on a Monte Carlo Simulation

Additional lenses implanted in the ciliary sulcus (AddOn) are one option for permanent correction of refractive error or generate pseudoaccommodation in the pseudophakic eye. The purpose of this paper was to model the power and magnification behaviour of toric AddOn and to show the effect sizes with a Monte Carlo simulation.

Anonymized data of a cataractous population uploaded for formula constant optimization were extracted from the IOLCon platform. After filtering out data with refractive spherical equivalent (RSEQ) between -0.75 and 0.25 dpt and refractive cylinder (RCYL) lower than 0.75, for each of the N = 6,588 records, a toric AddOn was calculated which transfers the refraction error from spectacle plane to AddOn plane using a matrix-based calculation strategy based on linear Gaussian optics. The equivalent (AddOnEQ) and toric (AddOnCYL) power of the AddOn and the overall lateral magnification change and meridional magnification were derived for the situations before and after AddOn implantation, and a linear modelling was fitted for all 4 parameters.

RSEQ is the dominant effect size in the prediction of AddOnEQ and overall change in magnification (ΔM), whereas the lens position (LP), corneal thickness (CCT), and mean corneal radius (CPa) play a minor role. In a simplified model, AddOnEQ can be estimated by 0.0179 + 1.4104 RSEQ. RCYL and corneal radius difference (CPad) are the dominant effect sizes in the prediction of AddOnCYL and the change in meridional magnification (ΔMmer), whereas LP, CCT, CPa, and RSEQ play a minor role. In a simplified model, AddOnCYL can be predicted by -0.0005 + 0.0328 CPad + 1.4087 RCYL. Myopic eyes gain in overall magnification, whereas in hyperopic eyes, we observe a loss. Meridional distortion could be in general reduced to 35% on average with a toric AddOn.

Our simulation shows that with a linear model, the equivalent and toric AddOn power, as well as overall change in magnification, meridional distortion before and after AddOn implantation, and the reduction in meridional distortion, can be easily predicted from the biometric data in pseudophakic eyes with moderate refractive error.