Translation model for CW chord to angle Alpha derived from a Monte-Carlo simulation based on raytracing

BACKGROUND: The Chang-Waring chord is provided by many ophthalmic instruments, but proper interpretation of this chord for use in centring refractive procedures at the cornea is not fully understood. The purpose of this study is to develop a strategy for translating the Chang-Waring chord (position of pupil centre relative to the Purkinje reflex PI) into angle Alpha using raytracing techniques. METHODS: The retrospective analysis was based on a large dataset of 8959 measurements of 8959 eyes from 1 clinical centre, using the Casia2 anterior segment tomographer. An optical model based on: corneal front and back surface radius Ra and Rp, asphericities Qa and Qp, corneal thickness CCT, anterior chamber depth ACD, and pupil centre position (X-Y position: Pup(X) and Pup(Y)), was defined for each measurement. Using raytracing rays with an incident angle I(X) and I(Y) the CW chord (CW(X) and CW(Y)) was calculated. Using these data, a multivariable linear model was built up in terms of a Monte-Carlo simulation for a simple translation of incident ray angle to CW chord. RESULTS: Raytracing allows for calculation of the CW chord CW(X)/CW(Y) from biometric measures and the incident ray angle I(X)/I(Y). In our dataset mean values of CW(X) = 0.32±0.30 mm and CW(Y) = -0.10±0.26 mm were derived for a mean incident ray angle (angle Alpha) of I(X) = -5.02±1.77° and I(Y) = 0.01±1.47°. The raytracing results could be modelled with a linear multivariable model, and the effect sizes for the prediction model for CW(X) are identified as Ra, Qa, Rp, CCT, ACD, Pup(X), Pup(Y), I(X), and for CW(Y) they are Ra, Rp, Pup(Y), and I(Y). CONCLUSION: Today the CW chord can be directly measured with any biometer, topographer or tomographer. If biometric measures of Ra, Qa, Rp, CCT, ACD, Pup(X), Pup(Y) are available in addition to the CW chord components CW(X) and CW(Y), a prediction of angle Alpha is possible using a simple matrix operation.