Abstract
Objective of the work is to investigate stress and deformation that conrneal tissue and donor graft undergo during endothelial keratoplasty. In order to attach the donor graft to the cornea, different air bubble pressure profiles acting on the graft are considered. This study is carried out by employing a three-dimensional nonlinear finite element methodology, combined with a contact algorithm. The ocular tissues are treated as isotropic, hyper-elastic and nearly-incompressible materials. The contact algorithm, based on the penalty-based node-to-surface approach, is used to model the donor graft-corneal interface region. First, the proposed computational methodology is tested against benchmark data for bending of the plates over a cylinder. Then, the influence of geometrical and material parameters of the graft on the corneal contact-structural response is investigated. The results are presented in terms of Von Mises stress intensity, displacement and mean contact force. Results clearly indicate that the air bubble pressure plays a key role in the corneal stress and strain, as well as graft stiffness and thickness.
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Abbreviations
- d :
-
Displacement vector (mm)
- e :
-
Tangent vector
- E :
-
Young’s Modulus (Pa)
- F :
-
Deformation gradient
- f :
-
Contact force (N)
- g i :
-
Gap vector (mm)
- N :
-
Normal vector
- K :
-
Stiffness matrix
- K c :
-
Contact stiffness matrix
- P :
-
Bubble pressure (Pa)
- R C :
-
Residual contact forces vector (N)
- S :
-
Internal forces vector (N)
- T :
-
External forces vector (N)
- t :
-
Traction vector (Pa)
- w :
-
Dual basis vector
- υ :
-
Poisson ratio
- ε :
-
Contact penalty parameter (N/mm)
- ρ :
-
Density (kg/m3)
- κ :
-
Incompressibility penalty parameter (Pa)
- μ :
-
Shear modulus (Pa)
- σ:
-
Cauchy Stress Tensor (Pa)
- Ψ:
-
Strain Energy function (Pa)
- AC:
-
Anterior chamber
- DM:
-
Descemet’s membrane
- VM:
-
Von Mises
- p:
-
Projection
- s:
-
Slave node
- max:
-
Maximum
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Alessandro Mauro gratefully acknowledges the local program of the University of Napoli “Parthenope” for the support to individual research.
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Mohamed, S., Coccarelli, A., Mauro, A. et al. A novel numerical modelling approach for keratoplasty eye procedure. Biomech Model Mechanobiol 18, 1429–1442 (2019). https://doi.org/10.1007/s10237-019-01156-y
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DOI: https://doi.org/10.1007/s10237-019-01156-y