Griffiths G W, Płociniczak Ł, Schiesser W E
City University, Northampton Square, London EC1V 0HB, UK.
Faculty of Pure and Applied Mathematics, Wrocław University of Science and Technology, Wyb. Wyspiańskiego 27, 50-370 Wrocław, Poland.
Comput Biol Med. 2016 Oct 1;77:274-84. doi: 10.1016/j.compbiomed.2016.08.011. Epub 2016 Aug 15.
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.
我们讨论了基于径向基函数（RBFs）的无网格方法来求解角膜曲率。引入了一个完整的二维非线性薄膜偏微分方程（PDE）模型，并使用多二次（MQ）和逆多二次（IMQ）径向基函数进行求解。这种新方法不依赖于角膜形状的径向对称性或其他简化假设。它还为角膜地形图建模方法提供了一种替代方案，后者需要准确的材料参数值，如杨氏模量和泊松比，而这些值可能无法获取。结果与已发表的角膜数据显示出良好的一致性，并允许进行反向计算以估计角膜的某些物理特性，如张力和弹性系数。所有计算和图形生成均使用R语言编程环境[34]和RStudio（R的集成开发环境（IDE））[36]完成，这两者都是开源且可免费下载的。本文的第二部分[48]展示了该方法如何用于对角膜测量数据集进行非常精确的拟合。
