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Background  Though the development and fitting of scleral contact lenses are expanding steadily, there is no simple method to provide scleral metrics for scleral contact lens fitting yet. The aim of this study was to establish formulae for estimation of the axial radius of curvature (ARC) of the anterior sclera using ocular biometric parameters that can be easily obtained with conventional devices.    Methods  A semi-automated stitching method and a computational analysis tool for calculating ARC were developed by using the ImageJ and MATLAB software. The ARC of all the ocular surface points were analyzed from the composite horizontal cross-sectional images of the right eyes of 24 volunteers; these measurements were obtained using anterior segment optical coherence tomography for a previous study (AS-OCT; Visante). Ocular biometric parameters were obtained from the same volunteers with slit-scanning topography and partial coherence interferometry. Correlation analysis was performed between the ARC at 8 mm to the axis line (ARC[8]) and other ocular parameters (including age). With ARC obtained on several nasal and temporal points (7.0, 7.5, 8.0, 8.5, and 9.0 mm from the axis line), univariate and multivariate linear regression analyses were performed to develop a model for estimating ARC with the help of ocular biometric parameters.    Results  Axial length, spherical equivalent, and angle kappa showed correlations with temporal ARC[8] (tARC[8]; Pearson’s  r  = 0.653, −0.579, and −0.341;  P  = 0.001, 0.015, and 0.015, respectively). White-to-white corneal diameter (WTW) and anterior chamber depth (ACD) showed correlation with nasal ARC[8] (nARC[8]; Pearson’s  r  = −0.492 and −0.461;  P  = 0.015 and 0.023, respectively). The formulae for estimating scleral curvatures (tARC, nARC, and average ARC) were developed as a function of axial length, ACD, WTW, and distance from the axis line, with good determinant power (72 − 80 %; SPSS ver. 22.0). Angle kappa showed strong correlation with axial length (Pearson’s  r  = −0.813,  P  <0.001), and the different correlation patterns of nasal and temporal ARC with axial length can be explained by the ocular surface deviation represented by angle kappa.    Conclusions  Axial length, ACD, and WTW are useful parameters for estimating the ARC of the anterior sclera, which is important for the haptic design of scleral contact lenses. Angle kappa affects the discrepancies between the nasal and temporal scleral curvature.    Electronic supplementary material  The online version of this article (doi:10.1186/s12886-016-0355-5) contains supplementary material, which is available to authorized users.

Estimation of axial curvature of anterior sclera: correlation between axial length and anterior scleral curvature as affected by angle kappa