Advertisement

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
  • 37 Downloads

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.

Keywords

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

List of symbols

d

Displacement vector (mm)

e

Tangent vector

E

Young’s Modulus (Pa)

F

Deformation gradient

f

Contact force (N)

gi

Gap vector (mm)

N

Normal vector

K

Stiffness matrix

Kc

Contact stiffness matrix

P

Bubble pressure (Pa)

RC

Residual contact forces vector (N)

S

Internal forces vector (N)

T

External forces vector (N)

t

Traction vector (Pa)

w

Dual basis vector

Greek symbols

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)

Acronyms

AC

Anterior chamber

DM

Descemet’s membrane

VM

Von Mises

Subscripts

p

Projection

s

Slave node

max

Maximum

Notes

Acknowledgements

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.

References

  1. Bonet J, Wood RD (2010) Nonlinear continuum mechanics for finite element analysis, 2nd edn. Cambridge University Press, CambridgezbMATHGoogle Scholar
  2. Canovetti A, Rossi F, Rossi M, Menabuoni L, Malandrini A, Pini R, Ferrara P (2018) Anvil-profiled penetrating keratoplasty: load resistance evaluation. Biomech Model Mechanobiol.  https://doi.org/10.1007/s10237-018-1083-y Google Scholar
  3. Doghri I, Muller A, Taylor RL (1998) A general three-dimensional contact procedure for implicit finite element codes. Eng Comput 15(2):233–259.  https://doi.org/10.1108/02644409810202639 CrossRefzbMATHGoogle Scholar
  4. Fraldi M, Cutolo A, Esposito L, Guarracino F (2011) The role of viscoelasticity and stress gradients on the outcome of conductive keratoplasty. Biomech Model Mechanobiol 10(3):397–412.  https://doi.org/10.1007/s10237-010-0242-6 CrossRefGoogle Scholar
  5. Gormsen A, Ivarsen A, Hjortdal J (2018) Retrospective single-center registry study on graft thickness 1 year after descemet stripping automated endothelial keratoplasty. Cornea.  https://doi.org/10.1097/ICO.0000000000001793 Google Scholar
  6. Holzapfel GA (2000) Non-linear solid mechanics: a continuum approach for engineering. Wiley, Chichester, p c2000Google Scholar
  7. Khan NH, Shiakolas PS (2016) Finite element analysis of Descemet’s Stripping Automated Endothelial Keratoplasty (DSAEK) surgery allograft to predict endothelial cell loss. Curr Eye Res 42(1):32–40.  https://doi.org/10.3109/02713683.2016.1151052 CrossRefGoogle Scholar
  8. Kopačka J, Gabriel D, Plešek J, Ulbin M (2015) Assessment of methods for computing the closest point projection, penetration, and gap functions in contact searching problems. Int J Numer Methods Eng 105(11):803–833.  https://doi.org/10.1002/nme.4994 MathSciNetCrossRefGoogle Scholar
  9. Lago MA, Rupérez MJ, Martínez-Martínez F, Monserrat C, Larra E, Güell JL, Peris-Martínez C (2010) A new methodology for the in vivo estimation of the elastic constants that characterize the patient-specific biomechanical behaviour of the human cornea. J Biomech 48(1):38–43.  https://doi.org/10.1016/j.jbiomech.2014.11.009 CrossRefGoogle Scholar
  10. Last JA, Liliensiek SJ, Nealey PF, Murphyaa CJ (2009) Determining the mechanical properties of human corneal basement membranes with atomic force microscopy. J Struct Biol 12:14.  https://doi.org/10.1016/j.jsb.2009.03.012 Google Scholar
  11. Laursen TA, Simo JC (1993) A continuum-based finite element formulation for the implicit solution of multibody, large deformation-frictional contact problems. Int J Numer Methods Eng 36(20):3451–3485.  https://doi.org/10.1002/nme.1620362005 MathSciNetCrossRefzbMATHGoogle Scholar
  12. Mauro A, Massarotti N, Salahudeen M, Una IR, Romano MR, Romano V (2018a) A novel patient-oriented numerical procedure for glaucoma drainage devices. Int J Numer Methods Biomed Eng 34(12):e3141.  https://doi.org/10.1007/s11517-018-1813-4 MathSciNetCrossRefGoogle Scholar
  13. Mauro A, Massarotti N, Salahudeen M, Romano MR, Romano V, Nithiarasu P (2018b) A generalised porous medium approach to study thermo-fluid dynamics in human eyes. Med Biol Eng Comput 56(10):1823–1839.  https://doi.org/10.1002/cnm.3141 CrossRefGoogle Scholar
  14. Mauro A, Romano MR, Romano V, Nithiarasu P (2018c) Suprachoroidal shunts for treatment of glaucoma: a comparison based on numerical simulations. Int J Numer Methods Heat Fluid Flow 28(2):297–314.  https://doi.org/10.1108/HFF-12-2016-0508 CrossRefGoogle Scholar
  15. Mauro A, Massarotti N, Salahudeen M, Cuomo F, Costagliola C, Ambrosone L, Romano MR (2018d) Design of a novel heating device for infusion fluids in vitrectomy. Appl Therm Eng 128:625–636.  https://doi.org/10.1016/j.applthermaleng.2017.08.027 CrossRefGoogle Scholar
  16. Montanino A, Angelillo M, Pandolfi A (2018) Modelling with a mesh free approach the cornea-aqueous humor interaction during the air puff test. J Mech Behav Biomed Mater 77:205–216.  https://doi.org/10.1016/j.jmbbm.2017.05.042 CrossRefGoogle Scholar
  17. Moshirfar M, Imbornoni LM, Muthappan V, Williams L, Khalifa YM, Jarstad A, Sikder S (2014) In vitro pilot analysis of uniformity, circularity, and concentricity of DSAEK donor endothelial grafts prepared by a microkeratome. Cornea 33(2):191–196.  https://doi.org/10.1097/ICO.0000000000000031 CrossRefGoogle Scholar
  18. Nguyen TD, Boyce BL (2011) An inverse finite element method for determining the anisotropic properties of the cornea. Biomech Model Mechanobiol 10(3):323–337.  https://doi.org/10.1007/s10237-010-0237-3 CrossRefGoogle Scholar
  19. Pandolfi A, Manganiello F (2006) A model for the human cornea: constitutive formulation and numerical analysis. Biomech Model Mechanobiol 5(4):237–246.  https://doi.org/10.1007/s10237-005-0014-x CrossRefGoogle Scholar
  20. Parekh M, Leon P, Ruzza A, Borroni D, Ferrari S, Ponzin D, Romano V (2018a) Graft detachment and rebubbling rate in descemet membrane endothelial keratoplasty. Surv Ophthalmol 63(2):245–250.  https://doi.org/10.1016/j.survophthal.2017.07.003 CrossRefGoogle Scholar
  21. Parekh M, Ruzza A, Kaye A, Steger B, Kaye SB, Romano V (2018b) Descemet Membrane Endothelial Keratoplasty-Complication and management of a single case for tissue preparation and graft size linked to post-op descemetorhexis disparity. Am J Ophthalmol Case Rep 12:65–67.  https://doi.org/10.1016/j.ajoc.2018.09.003 CrossRefGoogle Scholar
  22. Shih P, Huang C, Huang T, Lin H, Yen J, Wang I, Cao H, Shih W, Dai C (2017) Estimation of the Corneal Young’s modulus in vivo based on a fluid-filled spherical-shell model with Scheimpflug Imaging. J Ophthalmol 15:5410143.  https://doi.org/10.1155/2017/5410143 Google Scholar
  23. Sinha RA, Dupps WJ Jr (2009) Effects of altered corneal stiffness on native and postoperative LASIK corneal biomechanical behavior: a whole-eye finite element analysis. J Refract Surg 25(10):875–887.  https://doi.org/10.3928/1081597X-20090917-09 CrossRefGoogle Scholar
  24. Stuart AJ, Romano V, Virgili G, Shortt AJ (2018) Descemet’s membrane endothelial keratoplasty (DMEK) versus Descemet’s stripping automated endothelial keratoplasty (DSAEK) for corneal endothelial failure. Cochrane Database of Syst Rev 6:CD012097.  https://doi.org/10.1002/14651858.CD012097.pub2 Google Scholar
  25. Studer H, Larrea X, Riedwyl H, Buchler P (2010) Biomechanical model of human cornea based on stromal microstructure. J Biomech 43:836–842.  https://doi.org/10.1016/j.jbiomech.2009.11.021 CrossRefGoogle Scholar
  26. Tan DT, Dart JK, Holland EJ, Kinoshita S (2012) Corneal transplantation. Lancet 79(9827):1749–1761.  https://doi.org/10.1016/S0140-6736(12)60437-1 CrossRefGoogle Scholar
  27. Whitford C, Studer H, Boote C, Meek KM, Elsheikh A (2015) Biomechanical model of the human cornea: considering shear stiffness and regional variation of collagen anisotropy and density. J Mech Behav Biomed Mater 42:76–87.  https://doi.org/10.1016/j.jmbbm.2014.11.006 CrossRefGoogle Scholar
  28. Zienkiewicz OC, Taylor RL, Zhu JZ (2013) The finite element method: its basis and fundamentals, 7th edn. Butterworths-Heinemann, OxfordzbMATHGoogle Scholar
  29. Zienkiewicz OC, Taylor RL, Fox D (2014) The finite element method for solid and structural mechanics, 7th edn. Butterworths-Heinemann, OxfordzbMATHGoogle Scholar

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

Personalised recommendations