Fig 1.
Schematic drawing of a left eye from above (the vertical coordinates are not shown in the plot).
The corneal front and back surface (with radius of curvature Ra and Rp and asphericity Qa and Qp respectively) are coaxially aligned with the Z axis of the coordinate system. The incident ray is tilted by angle IX (negative values for IX as the ray is tilted to nasally). The location of the pupil centre (PupX) is used to calculate the location of the pupil centre at the corneal apex plane (PupCX). PurkinjeCX refers to the projection of the Purkinje image PI at the corneal apex plane. Coordinates PurkinjeCX and PupCX are rotated to a plane perpendicular to the entrance beam ro read out the coordinates PurkinjeRX and PupRX as determined by the tomographer. The Chang Waring chord CWX is derived from the coordinate points of PurkinjeRX and PupRX. CCT / ACD / Pup refer to the central corneal thickness / the anterior chamber depth as the distance from the anterior corneal apex to the front apex of the crystalline lens / the pupil size as measured with the Casia 2 tomographer.
Table 1.
Explorative data extracted from the dataset of the Casia2 anterior segment tomograph.
Ra, Qa, Rp, Qp, CCT, ACD, Pup, PupX, PupY, IX, IY refer to the corneal front surface curvature and asphericity, corneal back surface curvature and asphericity, central corneal thickness, anterior chamber depth measured from the corneal front apex, lateral position of the pupil centre in X (positive values in the nasal direction) and Y (positive valuesin the superior direction), and simulated incident ray angle in X and Y. Right eyes were flipped in X. MEAN, SD, MEDIAN, 5% CL, and 95% CL refer to mean value, standard deviation, median, and 90% confidence interval, respectively.
Table 2.
Explorative data after raytracing and processing: PupCX, PupCY, PurkinjeCX, Purkinje CY, CWX, CWY refer to the horizontal and vertical coordinates of the pupil centre, Purkinje reflex PI, and Chang-Waring chord as would be noticed by an anterior segment analyser under patient fixation with a far target (projected from Cartesian coordinates X / Y / Z to a plane perpendicular to the incident ray).
EllipseRX, EllipseRY, Dlong, and Dshort refer to the horizontal and vertical coordinates of the centre and the long and short diameter of the constraint ellipse of the pupil outline derived from raytracing with a bundle of 10,000 rays. Right eyes were flipped in X. MEAN, SD, MEDIAN, 5% CL, and 95% CL refer to mean value, standard deviation, median, and 90% confidence interval, respectively.
Fig 2.
Matrix of grouped scatterplots for the relevant input parameters of the multivariable linear prediction model and the components of the CW chord (CWX in red, CWY in green).
The respective histograms are plotted on the diagonal of the matrix. The relevant effect sizes for CWX are identified with a stepwise fit algorithm to anterior and posterior corneal curvature Ra and Rp, asphericity of corneal front surface Qa, central corneal thickness CCT, anterior chamber depth ACD, position of the pupil centre PupX and PupY, and incident ray angle IX. The relevant effect sizes for CWY are identified to anterior and posterior corneal curvature Ra and Rp, position of the pupil centre PupY, and incident ray angle IY. The model is based on a dataset with N = 8959 eye measurements.
Fig 3.
Performance of the linear models: In the left graph the predicted Chang-Waring chord from the linear multivariable model (X and Y components CWXM and CWYM) is plotted versus the respective components derived from raytracing calculations (X and Y components CWX and CWY).
In the right graph the reverse model is shown, where the predicted incident ray angle from the linear multivariable model (X and Y components IXM and IYM) is plotted versus the respective components derived from raytracing calculations (X and Y components IX and IY). The model is based on a dataset with N = 8959 eye measurements.