Monte-Carlo-Simulation biometrischer Effektgrößen und deren Einfluss auf das Übersetzungsverhältnis des Hornhautastigmatismus in den Zylinder torischer Intraokularlinsen [Monte Carlo simulation of biometric effect sizes and their influence on the translational ratio of corneal astigmatism in the cylinders of toric intraocular lenses]

Background and objective Toric intraocular lenses (IOL) provide a reliable and predictable option for permanent correction of corneal astigmatism. In order to determine the lens strength necessary for achieving the desired correction, the operator can either use the calculation mode implemented in the biometry device or the calculation service offered by the lens manufacturer; however, in many cases a classical lens calculation from biometric data is not carried out but only a simplified estimation, which translates the corneal astigmatism into the torus of the toric IOL. This translational ratio, which is mostly used as an average standard value, can however show a substantial range of variation, so that in a worst case scenario an undercorrection of the refractive cylinder of up to 12.5 & x202f;% or an overcorrection of up to 17 & x202f;% can result. The purpose of this study was to elaborate the biometric effect sizes which determine the relationship between the corneal astigmatism to be corrected and the torus necessary for a full correction of an IOL. Methods A total of 16,744 datasets were extracted from the IOLCon web platform and initially the axial position of the IOL implant was derived independent of a formula, based on the preoperative biometric values and the postoperative spherical equivalent. Subsequently, based on a ray propagation strategy for spherocylindrical vergences, the corresponding refractive value of a full correcting toric IOL was calculated. The translational relationship as a ratio between lens toricity and corneal astigmatism was analyzed for potential biometric effect sizes with a Monte Carlo simulation. Results The Monte Carlo simulation showed that the ratio of lens toricity to corneal astigmatism cannot be assumed as being constant. The analyzed data revealed an average translational ratio of 1.3938 & x202f;+/- 0.0595 (median 1.3921) with a range from 1.2131 to 1.5974. The axial position of the IOL was found to have the greatest influence, whereby the more posterior the lens position the higher the ratio. Due to the correlation of axial eye length and axial lens position, the eye length can be assumed to be an indirect effect size. The corneal equivalent refractive strength and the corneal astigmatism have no noteworthy effect on the translational ratio. Conclusion Many calculation tools on the market simplify toric IOL power calculation by assuming a constant ratio of lens toricity to corneal astigmatism; however, the present simulation study showed that such a simplification can lead to clearly incorrect results. Accordingly, an individual calculation of IOL toricity based on biometric parameters (e.g. based on vergence propagation matrices or full aperture ray tracing) is recommended.