A novel numerical modelling approach for keratoplasty eye procedure

  • Salahudeen MohamedEmail author
  • Alberto Coccarelli
  • Alessandro Mauro
  • Nicola Massarotti
  • Mario R. Romano
  • Vito Romano
  • Perumal Nithiarasu
Original Paper


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.


Keratoplasty Cornea transplantation Biomechanics Hyper-elastic model Finite element method Contact mechanics 

List of symbols


Displacement vector (mm)


Tangent vector


Young’s Modulus (Pa)


Deformation gradient


Contact force (N)


Gap vector (mm)


Normal vector


Stiffness matrix


Contact stiffness matrix


Bubble pressure (Pa)


Residual contact forces vector (N)


Internal forces vector (N)


External forces vector (N)


Traction vector (Pa)


Dual basis vector

Greek symbols


Poisson ratio


Contact penalty parameter (N/mm)


Density (kg/m3)


Incompressibility penalty parameter (Pa)


Shear modulus (Pa)


Cauchy Stress Tensor (Pa)


Strain Energy function (Pa)



Anterior chamber


Descemet’s membrane


Von Mises





Slave node





Alessandro Mauro gratefully acknowledges the local program of the University of Napoli “Parthenope” for the support to individual research.

Compliance with ethical standards

Conflict of interest

The authors have no conflict of interest in the materials discussed in this work.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Salahudeen Mohamed
    • 1
    Email author
  • Alberto Coccarelli
    • 2
  • Alessandro Mauro
    • 1
  • Nicola Massarotti
    • 1
  • Mario R. Romano
    • 3
  • Vito Romano
    • 4
    • 5
  • Perumal Nithiarasu
    • 2
  1. 1.Dipartimento di IngegneriaUniversità degli Studi di Napoli “Parthenope”NaplesItaly
  2. 2.Zienkiewicz Centre for Computational Engineering, College of EngineeringSwansea UniversitySwanseaUK
  3. 3.Department of Biomedical SciencesHumanitas UniversityMilanItaly
  4. 4.Department of Eye and Vision Science, Institute of Ageing and Chronic DiseaseUniversity of LiverpoolLiverpoolUK
  5. 5.Instituto Universitario Fernandez-VegaUniversidad de Oviedo, Fundacion de Investigacion on OftalmologicaOviedoSpain

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