For citation:
Le V. Features of using optimization algorithms for personalizing the geometric and biomechanical parameters of the cornea model. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2026, vol. 26, iss. 1, pp. 56-67. DOI: 10.18500/1816-9791-2026-26-1-56-67, EDN: MLCWLX
Features of using optimization algorithms for personalizing the geometric and biomechanical parameters of the cornea model
This study explores the personalization of a 3D finite element model of the cornea for diagnosing its biomechanical properties in keratoconus and predicting treatment outcomes. A key limitation of existing models is their reliance on averaged parameters, which fail to account for individual patient variations and the presence/distribution of areas of reduced stiffness in keratoconus. Using clinical data from 256 eyes obtained with Pentacam AXL and Corvis ST, a methodology for building personalized 3D models in COMSOL Multiphysics was developed. The hyperelastic Yeoh material model, demonstrating the lowest error, was used. Specialized optimization algorithms were applied for different tasks. The Interior Point Optimizer (IPOPT) determined the undeformed configuration under intraocular pressure. The Levenberg-Marquardt algorithm identified the material parameters of healthy tissue based on Corvis ST dynamic tonometry data. Finally, the Nelder-Mead algorithm characterized local areas of reduced stiffness using corneal topography data. The model provides high accuracy, with root mean square deviation between modeled and measured geometric parameters below 0.1% and a correlation coefficient of 0.94 between modeled and measured deformation parameters.
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