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Analysis of cornea curvature using radial basis functions - Part I: Methodology
G W Griffiths1, Ł Płociniczak2, W E Schiesser3
1City University, Northampton Square, London EC1V 0HB, UK.
Computers in Biology and Medicine
|September 12, 2016
Summary
This study introduces a novel meshless method using radial basis functions (RBFs) to accurately model cornea curvature. The approach bypasses the need for simplifying assumptions and material properties, offering a new tool for corneal analysis.
Area of Science:
- Ophthalmology
- Biomedical Engineering
- Computational Science
Background:
- Corneal curvature modeling is crucial for understanding vision and designing treatments.
- Existing methods often rely on simplifying assumptions about cornea shape or require unavailable material properties.
Purpose of the Study:
- To develop and validate a novel meshless method for solving cornea curvature.
- To provide an alternative to traditional corneal topography methods.
- To enable estimation of corneal physical properties.
Main Methods:
- A two-dimensional nonlinear thin membrane partial differential equation (PDE) model was developed.
- The model was solved using multiquadratic (MQ) and inverse multiquadratic (IMQ) radial basis functions (RBFs).
- The method was implemented using the R programming language and RStudio.
Main Results:
- The RBF-based meshless method accurately models cornea curvature without requiring radial symmetry.
- Results show good agreement with published corneal data.
- The method allows for back-calculation of corneal physical properties like tension and elasticity.
Conclusions:
- The proposed meshless RBF method offers a robust and flexible approach to corneal curvature modeling.
- This technique provides an alternative for situations where material properties are unknown.
- The method has demonstrated high accuracy in fitting measured corneal data.
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