Finite element modelling of cornea mechanics: a
               review

The cornea is a transparent tissue in front of the eye that refracts light and facilitates vision. A slight change in the geometry of the cornea remarkably affects the optical power. Because of this sensitivity, biomechanical study of the cornea can reveal much about its performance and function. In vivo and in vitro studies have been conducted to investigate the mechanics of the cornea and determine its characteristics. Numerical techniques such as the finite element method (FEM) have been extensively implemented as effective and noninvasive methods for analyzing corneal mechanics and possible disorders. This article reviews the use of FEM for assessing the mechanical behavior of the cornea. Different applications of FEM in corneal disease studies, surgical predictions, impact simulations, and clinical applications have been reviewed. Some suggestions for the future of this type of modeling in the area of corneal mechanics are also discussed.

Finite element analysis; Cornea/physiology; Cornea/ultrastructure; Cornea/surgery; Biomechanics/methods; Models, biological

Authorship

Talisa Mohammad Nejad

Department of Civil and Materials Engineering, University of Illinois at Chicago, Chicago, IL 60607 USAUniversity of Illinois at ChicagoUSAChicago, IL, USADepartment of Civil and Materials Engineering, University of Illinois at Chicago, Chicago, IL 60607 USA

Craig Foster Correspondence address: Craig Foster. Department of Civil and Materials Engineering. University of Illinois at Chicago. MC 246, 3085 Engineering Research Facility - 842 W. Taylor St. - Chicago, IL 60607 - USA - E-mail: fosterc@uic.edu

Dipika Gongal

Foster Wheeler North America, Hampton, NJ 08827Foster Wheeler North AmericaHampton, NJFoster Wheeler North America, Hampton, NJ 08827

Correspondence address: Craig Foster. Department of Civil and Materials Engineering. University of Illinois at Chicago. MC 246, 3085 Engineering Research Facility - 842 W. Taylor St. - Chicago, IL 60607 - USA - E-mail: fosterc@uic.edu

Disclosure of potential conflicts of interest: T.M. Nejad, grant from National Institutes of Health; C. Foster, grant from National Institutes of Health; D. Gongal, None

SCIMAGO INSTITUTIONS RANKINGS

Foster Wheeler North America, Hampton, NJ 08827Foster Wheeler North AmericaHampton, NJFoster Wheeler North America, Hampton, NJ 08827

Figures

Figures (4)

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Figure 1
Common shell and solid elements used for finite element analysis (FEA) of the cornea. A) Triangle and B) quadrilateral are common shell elements. Each shell element node has 5 degrees of freedom (DOF): 3 translational and 2 rotations (approximately 2 orthogonal axes on the shell surface). C) Tetrahedral and D) hexahedral are common 3D elements. Each element node has 3 translational DOF.

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Figure 2
An example of a finite element (FE) mesh of the cornea using hexahedral elements.

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Figure 3
Schematic of boundary conditions at the limbus used by researchers. A) The cornea is constrained against displacement and rotation, as proposed in⁽⁵5. Alastrué V, Calvo B, Peña EM, Doblaré M. Biomechanical modeling of refractive corneal surgery. J Biomech Eng. 2006;128:150-60.⁾. B) The cornea is fixed against displacement, but may rotate at the edges, as in⁽²2. Pandolfi A, Holzapfel GA. Three-dimensional modeling and computational analysis of the human cornea considering distributed collagen fibril orientations. J Biomech Eng. 2008;130(6):061006.⁾. C) Springs normal to the cross-section. Researchers in⁽¹³13. Pandolfi A, Fotia G, Manganiello F. Finite element simulations of laser refractive corneal Surgery. Eng Comput. 2009;25:15-24.⁾ investigated boundary conditions (a), (b), and (c). D) The cornea is allowed to expand along a given surface, as in⁽¹¹11. Caravalho LA, Prado M, Cunha RH, Costa Neto A, Paranhos A, Schor P, et al. Keratoconus prediction using a finite element model of the cornea with local biomechanical properties. Arq Bras Oftalmol. 2009;72(2):139-45.^, ²³23. Anderson K, El-Sheikh A, Newson T. Application of structural analysis to the mechanical behaviour of the cornea. J R Soc Interface. 2004;1(1):3-15.^, ³⁷37. Elsheikh A, Geraghty B, Rama P, Campanelli M, Meek KM. Characterization of age-related variation in corneal biomechanical properties. J R Soc Interface. 2010;7(51):1475-85.^, ³⁸38. Fraldi M, Cutolo A, Esposito L, Guarracino F. The role of viscoelasticity and stress gradients on the outcome of conductive keratoplasty. Biomech Model Mechanobiol. 2011;10(3):397-412.⁾. Forty degrees from horizontal is taken as a typical angle.

Thumbnail

Figure 4
An example of vertical displacement mapping of a mouse cornea subjected to intraocular pressure (IOP) obtained from finite element (FE) simulations is shown in the cross-section. The wireframe on the bottom is the undeformed mesh, and vertical displacement colored by magnitude is shown on top. The corneal displacement, but not rotation, is restricted along the limbus.

Figure 1 Common shell and solid elements used for finite element analysis (FEA) of the cornea. A) Triangle and B) quadrilateral are common shell elements. Each shell element node has 5 degrees of freedom (DOF): 3 translational and 2 rotations (approximately 2 orthogonal axes on the shell surface). C) Tetrahedral and D) hexahedral are common 3D elements. Each element node has 3 translational DOF.

Figure 2 An example of a finite element (FE) mesh of the cornea using hexahedral elements.

Figure 3 Schematic of boundary conditions at the limbus used by researchers. A) The cornea is constrained against displacement and rotation, as proposed in⁽⁵5. Alastrué V, Calvo B, Peña EM, Doblaré M. Biomechanical modeling of refractive corneal surgery. J Biomech Eng. 2006;128:150-60.⁾. B) The cornea is fixed against displacement, but may rotate at the edges, as in⁽²2. Pandolfi A, Holzapfel GA. Three-dimensional modeling and computational analysis of the human cornea considering distributed collagen fibril orientations. J Biomech Eng. 2008;130(6):061006.⁾. C) Springs normal to the cross-section. Researchers in⁽¹³13. Pandolfi A, Fotia G, Manganiello F. Finite element simulations of laser refractive corneal Surgery. Eng Comput. 2009;25:15-24.⁾ investigated boundary conditions (a), (b), and (c). D) The cornea is allowed to expand along a given surface, as in⁽¹¹11. Caravalho LA, Prado M, Cunha RH, Costa Neto A, Paranhos A, Schor P, et al. Keratoconus prediction using a finite element model of the cornea with local biomechanical properties. Arq Bras Oftalmol. 2009;72(2):139-45.^, ²³23. Anderson K, El-Sheikh A, Newson T. Application of structural analysis to the mechanical behaviour of the cornea. J R Soc Interface. 2004;1(1):3-15.^, ³⁷37. Elsheikh A, Geraghty B, Rama P, Campanelli M, Meek KM. Characterization of age-related variation in corneal biomechanical properties. J R Soc Interface. 2010;7(51):1475-85.^, ³⁸38. Fraldi M, Cutolo A, Esposito L, Guarracino F. The role of viscoelasticity and stress gradients on the outcome of conductive keratoplasty. Biomech Model Mechanobiol. 2011;10(3):397-412.⁾. Forty degrees from horizontal is taken as a typical angle.

Figure 4 An example of vertical displacement mapping of a mouse cornea subjected to intraocular pressure (IOP) obtained from finite element (FE) simulations is shown in the cross-section. The wireframe on the bottom is the undeformed mesh, and vertical displacement colored by magnitude is shown on top. The corneal displacement, but not rotation, is restricted along the limbus.

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[1] Correspondence address: Craig Foster. Department of Civil and Materials Engineering. University of Illinois at Chicago. MC 246, 3085 Engineering Research Facility - 842 W. Taylor St. - Chicago, IL 60607 - USA - E-mail: fosterc@uic.edu