Three-dimensional modeling and computational analysis of the human cornea considering distributed collagen fibril orientations

Journal of Biomechanical Engineering

Volumn 130, Issue 6, 2008, Pages

  Pandolfi, Anna ^a   Holzapfel, Gerhard A ^b,c  

^a POLITECNICO DI MILANO   (Italy)

^b GRAZ UNIVERSITY OF TECHNOLOGY   (Austria)

^c ROYAL INSTITUTE OF TECHNOLOGY   (Sweden)

Author keywords

Anisotropy; Constitutive model; Cornea; Distributed collagen fibrils; Finite element method

Indexed keywords

COMPUTATIONAL ANALYSES; COMPUTATIONAL MODELS; CORNEA; CORNEAL THICKNESSES; DISTRIBUTED COLLAGEN FIBRILS; EXPERIMENTAL TESTS; FIBRILLAR STRUCTURES; HUMAN CORNEAS; INTRAOCULAR PRESSURES; MATERIAL PROPERTIES; MATERIAL STRUCTURES; MECHANICAL RESPONSES; MISES STRESSES; NONLINEAR REGIMES; REFRACTIVE POWERS; REFRACTIVE PROPERTIES; TOP SURFACES;

ANISOTROPY; COLLAGEN; COMPUTATIONAL GEOMETRY; MECHANICAL PROPERTIES; MODEL STRUCTURES; OPTICAL PROPERTIES; THREE DIMENSIONAL;

FINITE ELEMENT METHOD;

FIBRILLAR COLLAGEN;

ARTICLE; BIOLOGICAL MODEL; COMPUTER SIMULATION; CORNEA; FINITE ELEMENT ANALYSIS; MECHANICAL STRESS; PHYSIOLOGY; PROTEIN CONFORMATION; ULTRASTRUCTURE; YOUNG MODULUS;

COMPUTER SIMULATION; CORNEA; ELASTIC MODULUS; FIBRILLAR COLLAGENS; FINITE ELEMENT ANALYSIS; MODELS, BIOLOGICAL; PROTEIN CONFORMATION; STRESS, MECHANICAL;

EID: 58149178762     PISSN: 01480731     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.2982251     Document Type: Article

References (43)

1. Kokott, W., 1938, "Über die Mechanisch-Funktionelle Strukturen des Auges," Albrecht von Graefes Arch. Ophthalmol., 138, pp. 424-485.
2. Daxer, A., and Fratzl, P., 1997, "Collagen Fibril Orientation in the Human Corneal Stroma and Its Implication in Keratoconus," Invest. Ophthalmol. Visual Sci., 38, pp. 121-129.
3. Löpping, B., and Weale. R. A., 1965, "Changes in Corneal Curvature Following Ocular Convergence," Vision Res., 5, pp. 207-215.
4. Boote, C., Dennis, S., Huang, Y., Quantock. A. J., and Meek, K. M., 2005, "Lamellar Orientation in Human Cornea in Relation to Mechanical Properties," J. Struct. Biol., 149, pp. 1-6.
5. Boote, C., Dennis, S., and Meek, K. M., 2004, "Spatial Mapping of Collagen Fibril Organisation in Primate Cornea: An X-ray Diffraction Investigation," J. Struct. Biol., 146, pp. 359-367.
6. Newton, R. H., and Meek, K. M., 1998a, "Circumcorneal Annulus of Collagen Fibrils in the Human Limbus," Invest. Ophthalmol. Visual Sci., 39, pp. 1125-1134.
7. Newton, R. H., and Meek, K. M., 1998b, "The Integration of the Corneal and Limbal Fibrils in the Human Eye," Biophys. J., 75, pp. 2508-2512.
8. Aghamohammadzadeh, H., Newton, R. H., and Meek, K. M., 2004, "X-Ray Scattering Used to Map the Preferred Collagen Orientation in the Human Cornea and Limbus," Structure (London), 12, pp. 249-256.
9. Maurice, D. M., 1969, "The Cornea and Sclera," The Eye, 2nd ed., H. Davison, ed., Academic, New York, pp. 489-600.
10. Buzard, K. A., 1992, "Introduction to Biomechanics of the Cornea," Refract. Corneal Surg., 8, pp. 127-138.
11. Höltzel, D. A., Altman, P., Buzard, K., and Choe, K., 1992. "Strip Extensiometry for Comparison of the Mechanical Response of Bovine, Rabbit, and Human Corneas," J. Biomech. Eng., 114, pp. 202-215.
12. Pinsky, P. M., and Datye, D. V., 1991, "A Microstructurally-Based Finite Element Model of the Incised Human Cornea," J. Biomech., 24, pp. 907-922.
13. Pinsky, P. M., and Datye, D. V., 1992, "Numerical Modeling of Radial, Astigmatic, and Hexagonal Keratotomy," Refract. Corneal Surg., 8, pp. 164-172.
14. Velinsky, S. A., and Bryant, M. R., 1992, "On The Computer-Aided and Optimal Design of Keratorefractive Surgery," Refract. Corneal Surg., 8, pp. 173-182.
15. Bryant, M. R., and McDonnell, P. J., 1996, "Constitutive Laws for Biomechanical Modeling of Refractive Surgery," J. Biomech. Eng., 118, pp. 473-481.
16. Pinsky, P. M., van der Heide, D., and Chernyak, D., 2005, "Computational Modeling of Mechanical Anisotropy in the Cornea and Sclera," J. Cataract Refractive Surg., 31, pp. 136-145.
17. Holzapfel, G. A., Gasser, T. C., and Ogden, R. W., 2000, "A New Constitutive Framework for Arterial Wall Mechanics and a Comparative Study of Material Models," J. Elast., 61, pp. 1-48.
18. Alastrué, V., Calvo, B., Peña, E. M., and Doblaré, M., 2006. "Biomechanical Modeling of Refractive Corneal Surgery," ASME J. Biomech. Eng., 128, pp. 150-160.
19. Pandolfi, A., and Manganiello, F, 2006, "A Model for the Human Cornea: Constitutive Formulation and Numerical Analysis," Biomech. Model. Mechanobiol., 5, pp. 237-246.
20. Pandolfi, A., Fotia, G., and Manganiello, F., 2008, "Finite Element Simulations of Laser Refractive Corneal Surgery," Eng. Comput., in press.
21. Anderson, K., El-Sheikh, A., and Newton, T., 2004, "Application of Structural Analysis to the Mechanical Behaviour of the Cornea," J. R. Soc., Interface, 1, pp. 3-15.
22. Li, L. Y., and Tighe, B., 2006, "The Anisotropic Material Constitutive Models for the Human Cornea," J. Struct. Biol., 153, pp. 223-230.
23. Elsheikh, A., and Wang, D., 2007, "Numerical Modelling of Corneal Biomechanical Behaviour," Comput. Methods Biomech. Biomed. Eng., 10, pp. 85-95.
24. Meek, K. M., Blamires, T., Elliott, G. F, Gyi, T. J., and Nave, C., 1987, "The Organisation of Collagen Fibrils in the Human Corneal Stroma: A Synchrotron X-Ray Diffraction Study," Curr. Eye Res., 6, pp. 841-846.
25. Meek, K. M., and Newton, R. H., 1999, "Organization of Collagen Fibrils in the Corneal Stroma in Relation to Mechanical Properties and Surgical Practice," J. Refract. Surg., 15, pp. 695-699.
26. Gasser, T. C., Ogden, R. W., and Holzapfel, G. A., 2006, "Hyperelastic Modelling of Arterial Layers With Distributed Collagen Fibre Orientations," J. R. Soc., Interface, 3, pp. 15-35.
27. Radner, W., Zehetmayer, M., Aufreiter, R., and Mallinger, R., 1998, "Interlacing and Cross-Angle Distribution of Collagen Lamellae in the Human Cornea," Cornea, 17, pp. 537-543.
28. Hjortdal, J. O., 1996, "Regional Elastic Performance of the Human Cornea," J. Biomech., 29, pp. 931-942.
29. Bryant, M. R., Szerenyi, K., Schmotzer, H., and McDonnell, P. J., 1994, "Corneal Tensile Strength in Fully Healed Radial Keratotomy Wounds," Invest. Ophthalmol. Visual Sci., 35, pp. 3022-3031.
30. Jayasuriya, A. C., Scheinbeim, J. I., Lubkin, V., Bennett, G., and Kramer, P., 2003, "Piezoelectric and Mechanical Properties in Bovine Cornea," J. Biomed. Mater. Res. A, 66A, pp. 260-265.
31. Wollensak, G., Spoerl, E., and Seiler, T., 2003, "Stress-Strain Measurements of Human and Porcine Corneas After Riboflavin-Ultraviolet-a-Induced Cross-Linking," J. Cataract Refractive Surg., 29, pp. 1780-1785.
32. Zeng, Y., Yang, J., Huang, K., Lee, Z., and Lee, X., 2001, "A Comparison of Biomechanical Properties Between Human and Porcine Cornea," J. Biomech., 34, pp. 533-537.
33. Kampmeier, J., Radt, B., Birngruber, R., and Brinkmann, R., 2000, "Thermal and Biomechanical Parameters of Porcine Cornea," Cornea, 19, pp. 355-363.
34. Boyce, B. L., Jones, R. E., Nguyen, T. D., and Grazier, J. M., 2007, "Stress-Controlled Viscoelastic Tensile Response of Bovine Cornea," J. Biomech., 40, pp. 2367-2376.
35. Holzapfel, G. A., Sommer, G., Gasser, T. C., and Regitnig, P., 2005a. "Determination of the Layer-Specific Mechanical Properties of Human Coronary Arteries With Non-Atherosclerotic Intimal Thickening, and Related Constitutive Modelling," Am. J. Physiol. Heart Circ. Physiol., 289, pp. H2048-H2058.
36. Holzapfel, G. A., Stadler, M., and Gasser, T. C., 2005b, "Changes in the Mechanical Environment of Stenotic Arteries During Interaction With Stents: Computational Assessment of Parametric Stent Design," J. Biomech. Eng., 127, pp. 166-180.
37. Holzapfel, G. A., 2000, "Nonlinear Solid Mechanics," A Continuum Approach for Engineering. Wiley, Chichester.
38. Demiray, H., 1972, "A Note on the Elasticity of Soft Biological Tissues," J. Biomech., 5, pp. 309-311.
39. 1998, Handbook of Grid Generation, J. F. Thompson, B. K. Soni, and N. P. Weatherill, eds., CRC, Boca Raton, FL.
40. Manganiello, F., 2006, "A Computational Model of the Human Cornea: A Predictive Approach to Refractive Surgery," Ph.D. thesis, Politecnico di Milano, Italy.
41. Dubbelman, M., Sicam, V. A., and Van der Heijde, G. L., 2006, "The Shape of the Anterior and Posterior Surface of the Aging Human Cornea," Vision Res., 46, pp. 993-1001.
42. Holzapfel, G. A., and Gasser, T. C., 2001, "A Viscoelastic Model for Fiber-Reinforced Composites at Finite Strains: Continuum Basis, Computational Aspects and Applications," Comput. Methods Appl. Mech. Eng., 190, pp. 4379-4403.
43. Elsheikh, A., and Anderson, K., 2005, "Comparative Study of Corneal Strip Extensometry and Inflation Tests." J. R. Soc., Interface, 2, pp. 177-185.