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: PupX and PupY), was defined for each measurement. Using raytracing rays with an incident angle IX and IY the CW chord (CWX and CWY) 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 CWX/CWY from biometric measures and the incident ray angle IX/IY. In our dataset mean values of CWX = 0.32±0.30 mm and CWY = -0.10±0.26 mm were derived for a mean incident ray angle (angle Alpha) of IX = -5.02±1.77° and IY = 0.01±1.47°. The raytracing results could be modelled with a linear multivariable model, and the effect sizes for the prediction model for CWX are identified as Ra, Qa, Rp, CCT, ACD, PupX, PupY, IX, and for CWY they are Ra, Rp, PupY, and IY. CONCLUSION: Today the CW chord can be directly measured with any biometer, topographer or tomographer. If biometric measures of Ra, Qa, Rp, CCT, ACD, PupX, PupY are available in addition to the CW chord components CWX and CWY, a prediction of angle Alpha is possible using a simple matrix operation.

Back-calculation of keratometer index based on OCT data and raytracing - a Monte Carlo simulation.

PURPOSE: This study aims to develop a raytracing-based strategy for calculating corneal power from anterior segment optical coherence tomography data and extracting the individual keratometer index, which converts the corneal front surface radius to corneal power. METHODS: A large OCT dataset (10,218 eyes of 8,430 patients) from the Casia 2 (Tomey, Japan) was post-processed in MATLAB (MathWorks, USA). Radius of curvature, asphericity of the corneal front and back surface, central corneal thickness and pupil size (aperture) were used to trace a bundle of rays through the cornea and derive the best focus plane. Corneal power was calculated with respect to the corneal front vertex plane, and the keratometer index was back-calculated using corneal power and front surface radius. Keratometer index was analysed in a multivariate linear model. RESULTS: The averaged resulting keratometer index was 1.3317 ± 0.0017 with a median of 1.3317 and range from 1.3233 to 1.3390. In a univariate model, only the front surface asphericity affected the keratometer index. The multivariate model for modelling the keratometer index using all 6 input parameters performed very well (RMS error: 5.54e-4, R2 : 0.90, significance vs. constant model: <0.0001). CONCLUSIONS: In the classical calculation, the keratometer index used for converting corneal radius to dioptric power uses several model assumptions. As these assumptions are not generally satisfied, corneal power cannot be calculated from corneal front surface radius alone. Considering all 6 input variables, the linear prediction model performs well and can be used if all input parameters are measured with a tomographer.