Analysis of cornea curvature using radial basis functions - Part I: Methodology.
We discuss the solution of cornea curvature using a meshless method based on radial basis functions (RBFs). A full two-dimensional nonlinear thin membrane partial differential equation (PDE) model is introduced and solved using the multiquadratic (MQ) and inverse multiquadratic (IMQ) RBFs. This new approach does not rely on radial symmetry or other simplifying assumptions in respect of the cornea shape. It also provides an alternative to corneal topography modeling methods requiring accurate material parameter values, such as Young's modulus and Poisson ratio, that may not be available. The results show good agreement with published corneal data and allow back calculations for estimating certain physical properties of the cornea, such as tension and elasticity coefficient. All calculations and generation of graphics were performed using the R language programming environment [34] and RStudio, the integrated development environment (IDE) for R [36], both of which are open source and free to download. Part II [48] of this paper demonstrates how the method has been used to provide a very accurate fit to a corneal measured data set.
City University, Northampton Square, London EC1V 0HB, UK. Electronic address: graham@griffiths1.com.
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Griffiths
Faculty of Pure and Applied Mathematics, Wrocław University of Science and Technology, Wyb. Wyspiańskiego 27, 50-370 Wrocław, Poland. Electronic address: lukasz.plociniczak@pwr.edu.pl.
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Płociniczak
Lehigh University, D118 Iacocca, 111 Research Drive, Bethlehem, PA 18015, USA. Electronic address: wes1@Lehigh.edu.
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Schiesser
D001696:Biomechanical Phenomena; D003315:Cornea / Q000000981:diagnostic imaging*; D019781:Corneal Topography / Q000379:methods*; D004548:Elasticity; D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods*
Cornea data-set; Corneal topography; Elasticity coefficient; Meshless method; Partial differential equation (PDE); R language; Radial basis function (RBF); Radius of curvature; Tension