Skip to main content
SpringerLink
Log in

A model for the human cornea: constitutive formulation and numerical analysis

  • Original paper
  • Published:
Biomechanics and Modeling in Mechanobiology Aims and scope Submit manuscript

Abstract

The human cornea (the external lens of the eye) has the macroscopic structure of a thin shell, originated by the organization of collagen lamellae parallel to the middle surface of the shell. The lamellae, composed of bundles of collagen fibrils, are responsible for the experimentally observed anisotropy of the cornea. Anomalies in the fibril structure may explain the changes in the mechanical behavior of the tissue observed in pathologies such as keratoconus. We employ a fiber-matrix constitutive model and propose a numerical model for the human cornea that is able to account for its mechanical behavior in healthy conditions or in the presence of keratoconus under increasing values of the intraocular pressure. The ability of our model to reproduce the behavior of the human cornea opens a promising perspective for the numerical simulation of refractive surgery.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Anderson K, El-Sheikh A, Newson T (2004) Application of structural analysis to the mechanical behavior of the cornea. J R Soc Interface 1:1–13

    Article  Google Scholar 

  • Bryant MR, Marchi V, Juhasz T (2000) Mathematical models of picosecond laser in situ keratomileusis for high myopia. J Refract Surg 16:155–162

    Google Scholar 

  • Bryant MR, McDonnell PJ (1996) Constitutive laws for biomechanical modeling of refractive surgery. J Biomech Eng 118:473–481

    Google Scholar 

  • Bryant MR, Szerenyi K, Schmotzer H, McDonnel PJ (1994) Corneal tensile strength in fully healed radial keratotomy wounds. Invest Ophthalmol Vis Sci 35:3022–3031

    Google Scholar 

  • Daxer A, Fratzl P (1997) Collagen fibril orientation in the human corneal stroma and its implication in keratoconus. Invest Ophthalmol Vis Sci 38:121–129

    Google Scholar 

  • Duffey RJ, Learning D (2003) US trends in refractive surgery: 2002 ISRS survey. J Refract Surg 19:357–363

    Google Scholar 

  • Duffey RJ, Learning D (2005) US trends in refractive surgery: 2003 ISRS/AAO survey. J Refract Surg 21:87–91

    Google Scholar 

  • Guarnieri FA (1999) Modelo biomecanico del ojo para diseno asistido por computadora de la cirurgua refractiva. PhD Thesis, Universidad Nacional del Litoral, Santa Fe, Argentina

    Google Scholar 

  • Hjortdal JO (1996) Regional elastic performance of the human cornea. J Biomech 29:931–942

    Article  Google Scholar 

  • Hoeltzel DA, Altman P, Buzard K, Choe K-I (1992) Strip extensiometry for comparison of the mechanical response of bovine, rabbit, and human corneas. J Biomech Eng 114:202–214

    Google Scholar 

  • Holzapfel GA (2000) Nonlinear solid mechanics: a continuum approach for engineering. Wiley, New York

    MATH  Google Scholar 

  • Holzapfel GA, Gasser TC, Ogden RW (2000) A new constitutive framework for arterial wall mechanics and a comparative study of material models. J Elast 61:1–48

    Article  MATH  MathSciNet  Google Scholar 

  • Holzapfel GA, Weizsäcker HW (1998) Biomechanical behavior of the arterial wall and its numerical characterization. Comp Biol Med 28:337–392

    Article  Google Scholar 

  • Huang Y, Tuft SJ, Meek M (1996) Histochemical and X-ray diffraction study of kerato conus epikeratoplasty, report of two cases. Cornea 15:320–328

    Article  Google Scholar 

  • Jayasuriya AC, Ghosh S, Scheinbeim JI, Lubkin V, Bennett G, Kramer P (2003) A study of piezoelectric and mechanical anisotropies of the human cornea. Biosens Bioelectron 18:381–387

    Article  Google Scholar 

  • Kaliske M (2000) A formulation of elasticity and viscoelasticity for fibre reinforced material at small and finite strains. Comput Methods Appl Mech Eng 185:225–243

    Article  MATH  Google Scholar 

  • Lanir Y (1979) A structural theory for the homogeneous biaxial stress-strain relationships in flat collagenous tissues. J Biomech 12: 423–436

    Article  Google Scholar 

  • Le Tallec P, Rahier C, Kaiss A (1993) Three-dimensional incompressible viscoelasticity in large strains: formulation and numerical approximation. Comput Methods Appl Mech Eng 109:233–258

    Article  MATH  MathSciNet  Google Scholar 

  • Meek KM, Newton RH (1999) Organization of collagen fibrils in the corneal stroma in relation to mechanical properties and surgical practice. J Refract Surgery 15:695–699

    Google Scholar 

  • Meek KM, Blamires T, Elliott GF, Gyi TJ, Nave C (1987) The organisation of collagen fibrils in the human corneal stroma: a synchroton X-ray diffraction study. Curr Eye Res 6:841–846

    Google Scholar 

  • Merodio J, Ogden RW (2003) Instabilities and loss of ellipticity in fiber-reinforced com pressible non-linearly elastic solids under plane deformation. Int J Solids Struct 40:4707–4727

    Article  MATH  MathSciNet  Google Scholar 

  • Merodio J, Ogden RW (2005) On tensile instabilities and ellipticity loss in fiber-reinforced incompressible non-linearly elastic solids. Mech Res Commun 32:290–299

    Article  MathSciNet  Google Scholar 

  • Newton RH, Meek KM (1998a) Circumcorneal annulus of collagen fibrils in the human limbus. Invest Ophthalmol Vis Sci 39:1125–1134

    Google Scholar 

  • Newton RH, Meek KM (1998b) The integration of the corneal and limbal fibrils in the human eye. Biophys J 75:2508–2512

    Google Scholar 

  • Petroll WM, Roy P, Chuong CJ, Hall B, Cavanagh HD, Jester JV (1996) Measure ment of surgically induced corneal deformations using three-dimensional confocal microscopy. Cornea 15:154–164

    Article  Google Scholar 

  • Pinsky PM, Datye DV (1991) A microstructurally-based finite element model of the incised human cornea. J Biomech 24:907–922

    Article  Google Scholar 

  • Pinsky PM, Datye DV (1992) Numerical modeling of radial, astigmatic and hexagonal keratotomy. Refract Corneal Surg 8:164–172

    Google Scholar 

  • Pinsky PM, van der Heide D, Chernyak D (2005) Computational modeling of mechanical anisotropy in the cornea and sclera. J Cataract Refract Surg 31:136–145

    Article  Google Scholar 

  • Rabinowitz YS (1998) Keratoconus. Surv Ophthalmo 42:297–319

    Article  Google Scholar 

  • Seiler T, Matallana M, Sendler S, Bende T (1992) Does Bowman’s layer determine the biomechanical properties of the cornea?. Refract Corneal Surg 8:139–142

    Google Scholar 

  • Shin TJ, Vito RP, Johnson LW, McCarey BE (1997) The distribution of strain in the human cornea. J Biomech 30:497–503

    Article  Google Scholar 

  • Simo JC, Miehe C (1992) Assocative coupled thermoplasticity at finite strains: Formula tion, numerical analysis and implementation. Comput Methods Appl Mech Eng 98:41–104

    Article  MATH  Google Scholar 

  • Soergel F, Jean B, Seiler T, Bende T, Mucke S, Pechhold W, Pels L (1995) Dynamic mechanical spectroscopy of the cornea for measurement of its viscoelastic properties in vitro. Ger J Ophthalmol 4:151–156

    Google Scholar 

  • Spencer AJM (1972) Deformations of fibre-reinforced materials. Oxford Science Research, Papers, Oxford University Press, Oxford

    MATH  Google Scholar 

  • Thompson JF, Soni BK, Weatherrill NP (1998) Handbook of Grid Generation. CRC Press, Boca Raton

    MATH  Google Scholar 

  • Treloar LRG (1975) The physics of rubber elasticty. Clarendon Press, Oxford

    Google Scholar 

  • Uchio E, Ohno S, Kudoh J, Aoki K, Kisielewicz LT (1999) Simulation model of an eyeball based on finite element analysis on a supercomputer. Br J Ophthalmol 83:1106–1111

    Article  Google Scholar 

  • Wang JQ, Zeng YJ, Li XY (2000) Influence of some operational variables on the radial keratotomy operation. Br J Ophthalmol 84:651–653

    Article  Google Scholar 

  • Wollensak G, Spoerl E, Seiler T (2003) Stress-strain measurements of human and porcine corneas after riboflavin-ultraviolet-a-induced cross-linking. J Cataract Refract Surg 29:1780–1785

    Article  Google Scholar 

  • Zeng Y, Yang J, Huang K, Lee Z, Lee X (2001) A comparison of biomechanical properties between human and porcine cornea. J Biomech 34:533–537

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Ingegneria Strutturale, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133, Milano, Italy

    A. Pandolfi & F. Manganiello

Authors
  1. A. Pandolfi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. F. Manganiello
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. Pandolfi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pandolfi, A., Manganiello, F. A model for the human cornea: constitutive formulation and numerical analysis. Biomech Model Mechanobiol 5, 237–246 (2006). https://doi.org/10.1007/s10237-005-0014-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10237-005-0014-x

Keywords

Search

Navigation