Calculating the power of toric phakic intraocular lenses

A toric phakic intraocular lens (IOL) implanted in the anterior or posterior chamber of the eye has the potential to correct high or excessive ametropia and astigmatism with high predictability of the postoperative refraction and preservation of phakic accommodation. The calculation of spherical phakic lenses has been described previously, but a formalism for estimating the power of toric phakic lenses has not yet been published. The purpose of this study is to describe a mathematical strategy for calculating toric phakic IOLs.

The method presented in this paper is based on vergence transformation in the paraxial Gaussian space. Parameters used for the calculations are the spherocylindrical spectacle refraction before implantation, corneal power (sphere and astigmatism) and (spherocylindrical) target refraction, together with the vertex distance and the predicted position of the phakic IOL. 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. The axes of the preoperative refraction, the target refraction and the corneal astigmatism are at random (not necessarily aligned).

The method was applied to two clinical examples. In example 1 we calculate the power of a phakic lens for the simple case, when the target refraction is plano and the axis of the preoperative refraction is aligned to the axis of the corneal astigmatism. In example 2, the cylindrical axis of the preoperative refraction is not aligned to the corneal astigmatism and the target refraction is spherocylindrical (and the axis of the target refraction is not aligned to the preoperative refractive cylinder or the corneal astigmatism). The calculations for both examples are described step-by-step and illustrated in a table.

The calculation scheme can be generalized to an unlimited number of crossed cylinders in the optical pathway. Based on paraxial raytracing, the spherical and cylindrical power as well as the orientation of the cylinder are determined from the preoperative refraction (including vertex distance), the corneal power, the intended target refraction (including vertex distance) and the predicted position of the phakic lens implant provided by the lens manufacturer. This calculation scheme can be easily implemented in a simple computer program (i.e. in Microsoft excel or matlab).