title: Analysis of cornea curvature using radial basis functions - Part II: Fitting to data-set.
abstract: In part I we discussed the solution of corneal curvature using a 2D meshless method based on radial basis functions (RBFs). In Part II we use these methods to fit a full nonlinear thin membrane model to a measured data-set in order to generate a topological mathematical description of the cornea. In addition, we show how these results can lead to estimations for corneal radius of curvature and certain physical properties of the cornea; namely, tension and elasticity coefficient. Again all calculations and graphics generation were performed using the R language programming environment. The model describes corneal topology extremely well, and the estimated properties fall well within the expected range of values. The method is straight forward to implement and offers scope for further analysis using more detailed 3D models that include corneal thickness.
authors: City University, Northampton Square, London, EC1V 0HB, UK. Electronic address: graham@griffiths1.com.
authors: G W
authors: GW
authors: Griffiths
authors: 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.
authors: Ł
authors: Ł
authors: Płociniczak
authors: Lehigh University, D118 Iacocca, 111 Research Drive, Bethlehem, PA 18015, USA. Electronic address: wes1@Lehigh.EDU.
authors: W E
authors: WE
authors: Schiesser
mesh_terms: D000328:Adult; D003315:Cornea / Q000000981:diagnostic imaging* / Q000502:physiology*; D019781:Corneal Topography / Q000379:methods*; D004548:Elasticity; D006801:Humans; D008954:Models, Biological
keywords: Cornea data-set; Corneal topography; Elasticity coefficient; Meshless method; Partial differential equation (PDE); Radial basis function (RBF); Radius of curvature; Tension