An inverse finite element method for determining the anisotropic properties of the cornea

Biomechanics and Modeling in Mechanobiology

Volumn 10, Issue 3, 2011, Pages 323-337

  Nguyen, T D ^a   Boyce, B L ^b  

^a Whiting School of Engineering   (United States)

^b SANDIA NATIONAL LABORATORIES   (United States)

Author keywords

Adjoint method; Anisotropy; Cornea; Finite element method; Inflation experiment

Indexed keywords

ANISOTROPY; COLLAGEN; IMAGE CORRELATION; INVERSE PROBLEMS; MAMMALS; SENSITIVITY ANALYSIS;

ADJOINT METHODS; ANISOTROPIC PROPERTY; CORNEA; DEGREES OF ANISOTROPY; DIGITAL IMAGE CORRELATIONS; DISPLACEMENT FIELD; INFLATION EXPERIMENTS; INVERSE FINITE ELEMENT METHODS; SURFACE DISPLACEMENT; SURFACE GEOMETRIES;

FINITE ELEMENT METHOD;

BOVINAE;

COLLAGEN;

ANIMAL; ANISOTROPY; ARTICLE; BIOMECHANICS; CATTLE; CHEMISTRY; CORNEA; FINITE ELEMENT ANALYSIS; PHYSIOLOGY; PRESSURE; PROBABILITY;

ANIMALS; ANISOTROPY; BIOMECHANICS; CATTLE; COLLAGEN; CORNEA; FINITE ELEMENT ANALYSIS; PRESSURE; PROBABILITY;

EID: 79957893215     PISSN: 16177959     EISSN: 16822978     Source Type: Journal    
DOI: 10.1007/s10237-010-0237-3     Document Type: Article

References (35)

1. H Aghamohammadzadeh RH Newton KM Meek 2005 X-ray scattering used to map the preferred collagen orientation in the human cornea and limbus Structure 12 249 256 (Pubitemid 38224547)
2. V Alastrué B Calvo E Pena M Doblaré 2006 Biomechanical modeling of refractive corneal surgery J Biomech Eng 128 150 160 10.1115/1.2132368
3. JE Bischoff 2006 Reduced parameter formulation for incorporating viscoelasticity into tissue level biomechanics Ann Biomed Eng 34 1164 1172 2283725 10.1007/s10439-006-9124-6 (Pubitemid 44078481)
4. C Boote S Dennis Y Huang AJ Quantock KM Meek 2005 Lamellar orientation in human cornea in relation to mechanical properties J Struct Biol 149 1 6 10.1016/j.jsb.2004.08.009 (Pubitemid 40051396)
5. C Boote S Dennis KM Meek 2004 Spatial mapping of collagen fibril organisation in primate cornea-an X-ray diffraction investigation J Struct Biol 146 359 367 10.1016/j.jsb.2003.12.009 (Pubitemid 38507437)
6. C Boote S Hayes S Jones AJ Qantock PM Hocking CF Inglehearn M Ali KM Meek 2007 Collagen organization in the chicken cornea and structural alterations in the retinopathy, globe enlarged (rge) phenotype-an x-ray diffraction study J Struct Biol 161 1 8 10.1016/j.jsb.2007.08.015 (Pubitemid 350298255)
7. BL Boyce JM Grazier RE Jones TD Nguyen 2008 Full-field deformation of bovine cornea under constrained inflation conditions Biomaterials 28 3896 3904 10.1016/j.biomaterials.2008.06.011
8. MR Bryant PJ McDonnell 1996 Constitutive laws for biomechanical modeling of refractive surgery J Biomech Eng 118 473 481 10.1115/1.2796033 (Pubitemid 26397082)
9. MR Bryant SA Velinsky 1991 Design of keratorefractive surgical procedures: radial keratotomy J Biomech Eng 113 150 157 (Pubitemid 21684349)
10. MR Bryant SA Velinsky ME Plesha GP Clarke 1987 Computer-aided surgical design in refractive keratotomy The CLO J 13 238 242 (Pubitemid 17142995)
11. DG Cogan 1951 Applied anatomy and physiology of the cornea Trans Am Ophthalmol Soc 55 329
12. A Daxer P Fratzl 1997 Collagen fibril orientation in the corneal stroma and its implications in keratoconous Invest Ophthalmol Vis Sci 38 121 129 (Pubitemid 27051531)
13. DE Freund RL McCally RA Farrell SM Cristol NL Lhernault HF Edelhauser 1995 Ultrastructure in anterior and posterior stroma of perfused human and rabbit corneas-relation to transparency Invest Ophthalmol Vis Sci 36 1508 1523
14. Fung YC (1993) Biomechanics: mechanical properties of living tissues. Springer, New York, NY
15. TC Gasser RW Ogden GA Holzapfel 2006 Hyperelastic modelling of arterial layers with distributed collagen fibre orientations J R Soc Interface 3 15 35 10.1098/rsif.2005.0073 (Pubitemid 46682201)
16. MJA Girard JC Downs 2009 Peripapillary and posterior scleral mechanics-part i: development of an anisotropic hyperelastic constitutive model J Biomech Eng 131 051011 10.1115/1.3113682
17. NH Gokhale PE Barbone AA Oberai 2008 Solution of the nonlinear elasticity imaging inverse problem: the compressible case Inverse Probl 24 045010 2425877 10.1088/0266-5611/24/4/045010
18. GG Gum KN Gelatt DN Miller EO Mackay 1998 Intraocular pressure in normal dairy cattle Vet Opthalmol 1 159 161 10.1046/j.1463-5224.1998.00017.x (Pubitemid 128490974)
19. KD Hanna FE Jouve GO Waring 1989 Preliminary computer simulation of the effects of radial keratotomy Arch Ophthalmol 107 911 918 (Pubitemid 19166369)
20. S Hayes C Boote J Lewis J Sheppard M Abahussin AJ Quantock C Purslow M Votruba KM Meek 2007 Comparative study of fibrillar collagen arrangement in the corneas of primates and other mammals Anat Rec 290 1542 1550 10.1002/ar.20613 (Pubitemid 350247098)
21. Holzapfel GA (2000) Nonlinear solid mechanics: a continuum approach for engineers. John Wiley and Sons, LTD, Chichester
22. Y Lanir 1983 Constitutive equations for fibrous connective tissues J Biomech 16 1 12 10.1016/0021-9290(83)90041-6 (Pubitemid 13125809)
23. DM Maurice 1957 The structure and transparency of the cornea J Physiol 136 263 286
24. Maurice DM (1984) The cornea and sclera. In: Davson H (eds) The eye. Academic Press, New York, pp 1-158
25. KM Meek T Blamiers GF Elliott TJ Gyi C Nave 1987 The organization of collagen fibrils in the human corneal stroma: a synchrotron X-ray diffraction study Curr Eye Res 6 841 846 10.3109/02713688709034853 (Pubitemid 17123202)
26. KM Meek SJ Tuft Y Huang PS Gill S Hayes RH Newton AJ Bron 2005 Changes in collagen orientation and distribution in keratoconus cornea Invest Ophthalmol Vis Sci 46 1948 1956 10.1167/iovs.04-1253
27. TD Nguyen RE Jones BL Boyce 2007 Modeling the anisotropic finite-deformation viscoelastic behavior of soft fiber-reinforced composites Int J Solids Struct 44 8366 8389 1167.74381 10.1016/j.ijsolstr.2007.06.020 (Pubitemid 47632568)
28. TD Nguyen RE Jones BL Boyce 2008 A nonlinear anisotropic viscoelastic model for the tensile behavior of the corneal stroma J Biomech Eng 130 041020 10.1115/1.2947399
29. AA Oberai NH Gokhale GR Feijoo 2003 Solution of inverse problems in elasticity imaging using the adjoint method Inverse Probl 19 297 313 1991790 1171.35490 10.1088/0266-5611/19/2/304
30. A Pandolfi G Fotia F Manganiello 2009 Finite element simulations of laser refractive corneal surgery Eng Comput 25 15 24 10.1007/s00366-008-0102-5
31. A Pandolfi G Holzapfel 2008 Three-dimensional modeling and computational analysis of the human cornea considering distributed collagen fibril orientations J Biomech Eng 130 061006 10.1115/1.2982251
32. A Pandolfi F Manganiello 2006 A model for the human cornea: constitutive formulation and numerical analysis Biomech Model Mechanobiol 5 237 246 10.1007/s10237-005-0014-x (Pubitemid 44618438)
33. PM Pinsky DV Datye 1991 A microstructurally-based finite element model of the incised human cornea J Biomech 24 907 922 10.1016/0021-9290(91)90169-N
34. PM Pinsky D van der Heide D Chernyak 2005 Computational modeling of mechanical anisotropy in the cornea and schlera J Cataract Refract Surg 31 136 145 10.1016/j.jcrs.2004.10.048 (Pubitemid 40260701)
35. MS Sacks 2003 Incorporation of experimentally-derived fiber orientation into a structural constitutive model for planar collagenous tissues J Biomech Eng 125 280 287 10.1115/1.1544508 (Pubitemid 36506143)