Background and purpose: The calculation of phakic lenses (PL) was described by van der Heijde et al. [Klin. Monatsbl. Augenheilkd (1988) Vol. 193, pp. 99-102], but a formalism for estimating relative magnification compared with spectacle correction and accommodation effects are not yet published. The purpose of this study was to describe a mathematical strategy for calculating PL and relative magnification as a function of object vergence (phakic accommodation).
Methods: Parameters used for the calculations are the spectacle refraction before and after (target refraction) surgery, the vertex distance, corneal refraction, and the predicted position of the phakic intraocular lens. The lens power is determined as the difference in vergences between the spectacle-corrected eye and the uncorrected eye at the reference plane of the predicted lens position. If we simplify the crystalline lens to a single refracting surface located at the principal plane of the crystalline lens, the vergence of the eye with spectacle correction and with PL is determined as a function of object distance [object vergence 0 D (infinity) to 10 D (object at a distance of 10 cm)] to evaluate accommodation effects of the crystalline lens.
Results: The method was applied to two clinical examples. In example 1 we calculated the power of a PL for correction of a 10-D myopia and determined the relative magnification and the vergence at the principal plane of the crystalline lens as a function of object vergence. Magnification gain increases with objects at near from 17% to 26%, whereas the vergence at the principal plane of the crystalline lens changes by 3.04 D less than in the spectacle-corrected eye. In example 2, a 20-D myopia was corrected with a PL. The gain in magnification changed from 33% to 58% with nearer objects. The change in vergence at the principal plane of the crystalline lens with objects at near was much higher with the PL compared with the spectacle correction, which implies that the refractive change necessary for focusing objects at near distance is much higher in the PL correction.
Conclusions: Even if the predictability of postoperative refraction with PL is comparable or better than in other methods of correcting high or excessive ametropia, the effects of lateral magnification change and accommodation have to be considered to avoid image-size disparities (aniseikonia) and to maintain binocular vision, especially with monocular PL implantation and anisometropia.