A closed-form structural model of planar fibrous tissue mechanics

Journal of Biomechanics

Volumn 42, Issue 10, 2009, Pages 1424-1428

  Raghupathy, Ramesh ^a   Barocas, Victor H ^b  

^a UNIVERSITY OF MINNESOTA   (United States)

^b University of Minnesota   (United States)

Author keywords

Soft tissue mechanics

Indexed keywords

ANALYTIC EVALUATION; CLOSED FORM; FIBER ORIENTATIONS; FIBER STRESS; FIBROUS TISSUE; FINITE ELEMENT SIMULATIONS; MECHANICAL BEHAVIOR; NUMERICAL INTEGRATIONS; SOFT TISSUE; SOFT-TISSUE MECHANICS; STRUCTURAL MODELS; TISSUE MECHANICS; VON MISES DISTRIBUTION;

FIBERS; MODEL STRUCTURES; SPACECRAFT; TISSUE;

MECHANICS;

ACCURACY; ANALYTIC METHOD; ARTICLE; BIOMECHANICS; FINITE ELEMENT ANALYSIS; MATHEMATICAL ANALYSIS; MATHEMATICAL MODEL; PRIORITY JOURNAL; QUANTITATIVE STUDY; SIMULATION; SOFT TISSUE; STRESS STRAIN RELATIONSHIP; STRUCTURAL EQUATION MODELING; TISSUE STRUCTURE; VON MISES DISTRIBUTION;

ANIMALS; BIOMECHANICS; COLLAGEN; CONNECTIVE TISSUE; FIBROBLASTS; HUMANS; MODELS, BIOLOGICAL; STRESS FIBERS; TISSUE ENGINEERING;

EID: 67649502891     PISSN: 00219290     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jbiomech.2009.04.005     Document Type: Article

References (25)

1. Abramowitz M., and Stegun I.A. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (1964), US Govt. Printing Office p. 1046
2. Baek S., Valentin A., and Humphrey J.D. Biochemomechanics of cerebral vasospasm and its resolution: II. Constitutive relations and model simulations. Annals of Biomedical Engineering 9 (2007) 1498-1509
3. Billiar K.L., and Sacks M.S. Biaxial mechanical properties of the native and glutaraldehyde-treated aortic valve cusp: Part II-A structural constitutive model. Journal of Biomechanical Engineering-Transactions of the ASME 4 (2000) 327-335
4. Bischoff J.E., Arruda E.M., and Grosh K. Finite element modeling of human skin using an isotropic, nonlinear elastic constitutive model. Journal of Biomechanics 6 (2000) 645-652
5. Bowes L.E., Jimenez M.C., Hiester E.D., Sacks M.S., Brahmatewari J., Mertz P., and Eaglstein W.H. Collagen fiber orientation as quantified by small angle light scattering in wounds treated with transforming growth factor-beta(2) and its neutalizing antibody. Wound Repair and Regeneration 3 (1999) 179-186
6. Chandran P.L., and Barocas V.H. Affine vs. non-affine fibril kinematics in collagen networks: theoretical studies of network behavior. Journal of Biomechanical Engineering (2006) 259-270
7. Chandran P.L., and Barocas V.H. Microstructural mechanics of collagen gels in confined compression: poroelasticity, viscoelasticity, and collapse. Journal of Biomechanical Engineering 2 (2003) 152-166
8. Driessen N.J., Mol A., Bouten C.V., and Baaijens F.P. Modeling the mechanics of tissue-engineered human heart valve leaflets. Journal of Biomechanics 2 (2007) 325-334
9. Freed A.D., Einstein D.R., and Vesely I. Invariant formulation for dispersed transverse isotropy in aortic heart valves: an efficient means for modeling fiber splay. Biomechanics and Modeling in Mechanobiology 2-3 (2005) 100-117
10. Gasser T.C., Ogden R.W., and Holzapfel G.A. Hyperelastic modelling of arterial layers with distributed collagen fibre orientations. Journal of the Royal Society, Interface/the Royal Society 6 (2006) 15-35
11. Hepworth D.G., Steven-fountain A., Bruce D.M., and Vincent J.F.V. Affine versus non-affine deformation in soft biological tissues, measured by the reorientation and stretching of collagen fibres through the thickness of compressed porcine skin. Journal of Biomechanics 3 (2001) 341-346
12. Jhun, C.-S., Evans, M.C., Barocas, V.H., Tranquillo, R.T., 2009. Fiber reorientation in planar biaxial loading of bioartificial tissues possessing prescribed alignment. Journal of Biomechanical Engineering. in press.
13. Kuhl E., Garikipati K., Arruda E.M., and Grosh K. Remodeling of biological tissue: mechanically induced reorientation of a transversely isotropic chain network. Journal of the Mechanics and Physics of Solids 7 (2005) 1552-1573
14. Lanir Y. Constitutive equations for fibrous connective tissues. Journal of Biomechanics 1 (1983) 1-12
15. Lanir Y. Constitutive equations for fibrous connective tissues. Journal of Biomechanics 1 (1982) 1
16. Mardia K.V., and Jupp P.E. Directional Statistics (2000), Wiley, New York p. 429
17. Marquez J.P. Fourier analysis and automated measurement of cell and fiber angular orientation distributions. International Journal of Solids and Structures (2006) 6413-6423
18. Palmer J.S., and Boyce M.C. Constitutive modeling of the stress-strain behavior of F-actin filament networks. Acta Biomaterialia 3 (2008) 597-612
19. Pinsky P.M., van der Heide D., and Chernyak D. Computational modeling of mechanical anisotropy in the cornea and sclera. Journal of Cataract and Refractive Surgery 1 (2005) 136-145
20. Sacks M.S. Incorporation of experimentally derived fiber orientation into a structural constitutive model for planar-collagenous tissues. Journal of Biomechanical Engineering-Transactions of the ASME 2 (2003) 280-287
21. Sander E.A., Tranquillo R.T., and Barocas V.H. Image-Based Biomechanics of Collagen-Based Tissue Equivalents: Multiscale Models Compared To Fiber Alignment Predicted by Polarimetric Imaging. IEEE Engineering in Medicine and Biology 28 3 (2009) 10-18
22. Sander E.A., and Barocas V.H. Comparison of 2D fiber network orientation measurement methods. Journal of Biomedical Materials Research 88A (2009) 322-331
23. Stylianopoulos T., and Barocas V.H. Multiscale, structure-based modeling for the elastic mechanical behavior of arterial walls. Journal of Biomechanical Engineering 4 (2007) 611-618
24. Tower T.T., Neidert M.R., and Tranquillo R.T. Fiber alignment imaging during mechanical testing of soft tissues. Annals of Biomedical Engineering 10 (2002) 1221-1233
25. Wagenseil J.E., and Okamoto R.J. Modeling cell and matrix anisotropy in fibroblast populated collagen vessels. Biomechanics and Modeling in Mechanobiology 3 (2007) 151-162