Numerical Verification Limits of Asymmetric Intrastromal Hydrogel Reinforcement for Decentered Keratoconus
Abstract
Spatially tailored intrastromal hydrogel scaffolds have been proposed for decentered keratoconus, but their mechanical and optical benefits require stringent numerical validation. We reanalyze conforming two-material finite-element benchmarks and earlier optomechanical screening calculations, distinguishing solver verification from constitutive adequacy and treatment efficacy. In a curved corneal-patch benchmark with a fixed-volume rectangular inclusion, the apparent peak-displacement benefit of an offset over a centered inclusion changes from -5.66% to +1.73% across four tetrahedral meshes, while absolute displacements remain strongly mesh dependent. On the finest mesh, the quadratic term in the Green-Lagrange strain tensor contributes about 18% of the root-mean-square magnitude of the linearized strain; the underlying finite-element solutions themselves remain linear elastic. Earlier optical screening was sensitive to corneal orientation, mesh refinement and wavefront-reference conventions and is not retained as validated evidence. These observations do not establish superiority of asymmetric reinforcement. Instead, they motivate prespecified criteria for geometry-invariant finite-strain simulations, two-material interface verification, optical wavefront convergence, and independent experimental validation. No clinical recommendation is implied.
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BibTeX
@misc{sumayamartinez2026numerical,
title = {{Numerical Verification Limits of Asymmetric Intrastromal Hydrogel Reinforcement for Decentered Keratoconus}},
author = {Juan Sumaya-Martínez and Alan Altamirano-Torres},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.01889},
eprint = {2611.01889},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.01889},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Numerical Verification Limits of Asymmetric Intrastromal Hydrogel Reinforcement for Decentered Keratoconus
AU - Juan Sumaya-Martínez
AU - Alan Altamirano-Torres
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.01889
UR - https://arxiv.org/abs/2611.01889
AB - Spatially tailored intrastromal hydrogel scaffolds have been proposed for decentered keratoconus, but their mechanical and optical benefits require stringent numerical validation. We reanalyze conforming two-material finite-element benchmarks and earlier optomechanical screening calculations, distinguishing solver verification from constitutive adequacy and treatment efficacy. In a curved corneal-patch benchmark with a fixed-volume rectangular inclusion, the apparent peak-displacement benefit of an offset over a centered inclusion changes from -5.66% to +1.73% across four tetrahedral meshes, while absolute displacements remain strongly mesh dependent. On the finest mesh, the quadratic term in the Green-Lagrange strain tensor contributes about 18% of the root-mean-square magnitude of the linearized strain; the underlying finite-element solutions themselves remain linear elastic. Earlier optical screening was sensitive to corneal orientation, mesh refinement and wavefront-reference conventions and is not retained as validated evidence. These observations do not establish superiority of asymmetric reinforcement. Instead, they motivate prespecified criteria for geometry-invariant finite-strain simulations, two-material interface verification, optical wavefront convergence, and independent experimental validation. No clinical recommendation is implied.
ER -