Iol Calculation Using Gaussian Optics With Clinical Precision And Scientific Transparency

IOL calculation formulae reach back to the late 1960ies. Until 2000, all calculation formulae have been scientifically published. They all use thin lens Gaussian Optics and include model assumptions that may be outdated. Furthermore, all of them were developed from ultrasound data. There are newer algorithms available that may give better clinical results or avoid trend errors. Unfortunately, these methods have neither been properly published nor disclosed. We want to present a non-commercial, open source kit formula that avoids most of the common problems and is open to extensions and improvements in it’s modules.

Private Eye Clinic

The Castrop formula is based on the basic vergence formulae of Gernet & Ostholt from 1970  with an added thick lens corneal model based on Liou & Brennan. When model errors are absent, the effective lens position (ELP) should be identical with the secondary principal plane of the IOL. Assuming that this plane is always inside the physical boundaries of a biconvex lens, we developed a regression model to predict the IOL equator plane from preoperative parameters. Non-linear machine learning models can also be used for this task. The indicated axial length (AL) is substituted by a back-calculated sum-of-segments AL according to Cooke. Either 2 or 3 constants adjust the ELP and the refractive offset independently.

The Castrop formula is superior to classical formulae in unselected eyes improving variance of prediction error by 37% on average. It is on par with all modern formulae for normal and long eyes and superior to most of them in short eyes. Trend errors are negligible.

As the formula is largely free from trend errors, it can be used for any eye without systematic deterioration or out-of-bounds-problems. ELP calculation is based on 1850 swept source OCT data sets avoiding unreliable back calculation from refractions. Adjustment of ELP and refractive offset are separated avoiding a typical problem of other IOL formulae. As 2 or 3 constants are used to adjust the IOL model, approx 200 cases per IOL model should be available for optimization. Alternatively, only the refractive offset can be adjusted when insufficient data is available. As the built-in corneal model can be substituted by an external total power model (e.g. from tomography software), it can also be used in post-LVC cases with great success.