The Castrop formula for calculation of toric intraocular lenses

Abstract

Purpose: To explain the concept behind the Castrop toric lens (tIOL) power calculation formula and demonstrate its application in clinical examples.

Methods: The Castrop vergence formula is based on a pseudophakic model eye with four refractive surfaces and three formula constants. All four surfaces (spectacle correction, corneal front and back surface, and toric lens implant) are expressed as spherocylindrical vergences. With tomographic data for the corneal front and back surface, these data are considered to define the thick lens model for the cornea exactly. With front surface data only, the back surface is defined from the front surface and a fixed ratio of radii and corneal thickness as preset. Spectacle correction can be predicted with an inverse calculation.

Results: Three clinical examples are presented to show the applicability of this calculation concept. In the 1st example, we derived the tIOL power for a spherocylindrical target refraction and corneal tomography data of corneal front and back surface. In the 2nd example, we calculated the tIOL power with keratometric data from corneal front surface measurements, and considered a surgically induced astigmatism and a correction for the corneal back surface astigmatism. In the 3rd example, we predicted the spherocylindrical power of spectacle refraction after implantation of any toric lens with an inverse calculation.

Conclusions: The Castrop formula for toric lenses is a generalization of the Castrop formula based on spherocylindrical vergences. The application in clinical studies is needed to prove the potential of this new concept.

Keywords: Castrop formula; Gaussian optics; Prediction of postoperative refraction; Toric intraocular lenses; Vergence calculation.

Fig. 1

Schematic model for the optical system of the pseudophakic eye. The model is defined by 4 refracting surfaces: a spectacle correction, corneal front and back surface, and intraocular lens. Vx refers to the spherocylindrical vergence in front of, and Vx′ to the spherocylindrical vergence behind, the refractive surface x. The effective lens position (ELP) is derived from the anterior chamber depth and the lens thickness of the phakic eye using formula constants C and H. SIA and CPA refer to the surgically induced astigmatism, both considered at the front apex plane of the cornea, and the refractive correction R (from the formula constant R) is considered at the spectacle plane

Fig. 2

Schematics of the calculation concept for toric intraocular lenses (left) and prediction of the refraction after implantation of a toric lens (right). Add_Surface () and Transform_Vergence () refer to functions of adding up a spherocylindrical surface to a vergence and tracing a spherocylindrical vergence through a homogeneous optical medium. The power of the toric lens implant is calculated from the difference of vergence V3′ and V3 (left), whereas the spherocylindrical refraction at the spectacle plane is derived from the difference of vergence V0′ and vergence (V0 − VR)