Microstructure-based, multiscale modeling for the mechanical behavior of hydrated fiber networks

Multiscale Modeling and Simulation

Volumn 7, Issue 1, 2008, Pages 22-43

  Chandran, Preethi L ^a   Stylianopoulos, Triantafyllos ^a   Barocas, Victor H ^a  

^a University of Minnesota   (United States)

Author keywords

Fibrous medium; Finite elements; Stokes flow; Tissue engineering; Volume averaging method

Indexed keywords

COLLAGEN; FIBERS; FLOW OF FLUIDS; GELS; INTEGRAL EQUATIONS; MICROSTRUCTURE; REYNOLDS NUMBER; STRAIN RATE; TISSUE ENGINEERING;

FIBROUS MEDIUM; FINITE-ELEMENT FIELDS; HYDRODYNAMIC INTERACTION; MULTISCALE FORMULATIONS; POROELASTIC MATERIALS; RECONSTITUTED COLLAGEN; STOKES FLOWS; VOLUME AVERAGING METHOD;

FINITE ELEMENT METHOD;

EID: 55149112098     PISSN: 15403459     EISSN: 15403467     Source Type: Journal    
DOI: 10.1137/070689504     Document Type: Article

References (42)

1. C. GUIDRY and F. GRINNELL, Contraction of hydrated collagen gels by fibroblasts: Evidence of two mechanisms by which collagen fibers are stabilized, Collagen and Related Research, 6 (1986), pp. 515-529.
2. T. D. ALLEN, S. L. SCHOR, and A. M. SCHOR, An ultrastructural review of collagen gels, a model system for cell-matrix, cell-basement membrane and cell-cell interactions, Scanning Electron. Microscopy, 1 (1984), pp. 375-390.
3. K. D. COSTA, E. J. LEE, and J. W. HOLMES, Creating alignment and anisotropy in engineered heart tissue: Role of boundary conditions in a model three-dimensional culture system, Tissue Eng., 9 (2003), pp. 567-577.
4. S. THOMOPOULOS, G. M. FOMOVSKY, and J. W. HOLMES, The development of structural and mechanical anisotropy in fibroblast populated collagen gels, J. Biomech. Eng., 127 (2005), pp. 742-750.
5. S. L. VOYTIK-HARBIN, B. P. RAIWA, and J. P. ROBINSON, 3D imaging of ECM and ECM-cell interactions, in Methods in Cell Biology: Cytometry, Z. Darzynkiewicz, H. A. Crissman, and J. P. Robinson, eds., Academic Press, San Diego, CA, 2000, pp. 583-596.
6. D. M. KNAPP, V. H. BAROCAS, T. T. TOWER, and R. T. TRANQUILLO, Estimation of cell traction and migration in an isometric cell traction assay, AIChE J., 45 (1999), pp. 2628-2640.
7. V. H. BAROCAS and R. T. TRANQUILLO, An anisotropic biphasic theory of tissue-equivalent mechanics: The interplay among cell traction, fibrillar network deformation, fibril alignment, and cell contact guidance, J. Biomech. Eng., 119 (1997), pp. 137-145.
8. B. COULOMB, L. DUBERTET, C. MERRILL, R. TOURAINE, and E. BELL, The collagen lattice: A model for studying the physiology, biosynthetic function and pharmacology of the skin, Bri. J. Dermatol., 111 (1984), pp. 83-87.
9. V. H. BAROCAS, T. S. GIRTON, and R. T. TRANQUILLO, Engineered alignment in media equivalents: Magnetic prealignment and mandrel compaction, J. Biomech. Eng., 120 (1998), pp. 660-666.
10. R. T. TRANQUILLO, Self-organization of tissue-equivalents: The nature and role of contact guidance, Biochem. Soc. Symp., 65 (1999), pp. 27-42.
11. P. L. CHANDRAN and V. H. BAROCAS, Microstructural mechanics of collagen gels in confined compression: Poroelasticity, viscoelasticity and collapse, J. Biomech. Eng., 126 (2004), pp. 152-166.
12. V. C. MOW, S. C. KUEI, W. M. LAI, and C. G. ARMSTRONG, Biphasic creep and stress relaxation of articular cartilage in compression. Theory and experiments, J. Biomech. Eng., 102 (1980), pp. 73-84.
13. C. G. ARMSTRONG, W. M. LAI, and V. C. MOW, An analysis of the unconfined compression of articular cartilage, J. Biomech. Eng., 106 (1984), pp. 165-173.
14. S. M. KLISCH and J. C. LOTZ, A special theory of biphasic mixtures and experimental results for human annulus fibrosus tested in confined compression, J. Biomech. Eng., 122 (2000), pp. 180-188.
15. W. M. LAI and V. C. MOW, Drag-induced compression of articular cartilage during a permeation experiment, Biorheology, 17 (1980), pp. 111-123.
16. R. M. BOWEN, Incompressible porous media models by use of the theory of mixtures, Internat. J. Engrg. Sci., 18 (1980), pp. 1129-1148.
17. J. C. SLATTERY, Flow of viscoelastic fluids through porous media, AIChE J., 13 (1967), pp. 1066-1071.
18. S. WHITAKER, The equations of motion in porous media, Chem. Eng. Sci., 21 (1966), pp. 291-300.
19. D. A. DREW, Averaged field equations for two-phase media, Studies in Appl. Math., 50 (1971), pp. 133-166.
20. G. H. CRAPISTE, E. ROTSTEIN, and S. WHITAKER, A general closure scheme for the method of volume averaging, Chem. Eng. Sci., 41 (1986), pp. 227-235.
21. G. H. GRAY, The derivation of equations for multi-phase flow, Chem. Eng. Sci., 30 (1975), pp. 229-233.
22. F. A. HOWES and S. WHITAKER, The spatial averaging theorem revisited, Chem. Eng. Sci., 40 (1985), pp. 1387-1392.
23. W. M. LAI, V. C. MOW, and V. ROTH, Effects of nonlinear strain-dependent permeability and rate of compression on the stress behavior of articular cartilage, J. Biomech. Eng., 103 (1981), pp. 61-66.
24. P. L. CHANDRAN and V. H. BAROCAS, Affine versus non-affine fibril kinematics in collagen networks: Theoretical studies of network behavior, J. Biomech. Eng., 128 (2006), pp. 259-270.
25. P. L. CHANDRAN and V. H. BAROCAS, Deterministic material-based averaging theory model of collagen gel mechanics, J. Biomech. Eng., 129 (2007), pp. 137-147.
26. T. STYLIANOPOULOS and V. H. BAROCAS, Volume-averaging theory for the study of the mechanics of collagen networks, Comput. Methods Appl. Mech. Engrg., 196 (2007), pp. 2981-2990.
27. T. STYLIANOPOULOS, C. A. BASHUR, A. S. GOLDSTEIN, S. A. GUELCHER, and V. H. BAROCAS, Computational predictions of the tensile properties of electrospun fiber meshes: Effect of fiber diameter and fiber orientation, J. Mech. Behav. Biomed. Mater., to appear.
28. T. STYLIANOPOULOS and V. H. BAROCAS, Multiscale, structure-based modeling for the elastic mechanical behavior of arterial walls, J. Biomech. Eng., 129 (2007), pp. 611-618.
29. S. WHITAKER, Diffusion and dispersion in porous media, AIChE J., 13 (1967), pp. 420-427.
30. S. WHITAKER, Flow in porous media III: Deformable media, Transp. Porous Media, 1 (1986), pp. 127-154.
31. R. T. TRANQUILLO, M. A. DURRANI, and G. A. MOON, Tissue engineering science: Consequences of cell traction force, Cytotechnology, 10 (1992), pp. 225-250.
32. S. WHITAKER, Flow in porous media I: A theoretical derivation of Darcy's law, Transp. Porous Media, 1 (1986), pp. 3-25.
33. R. G. COX, The motion of long slender bodies in a viscous fluid. Part 1. General theory, J. Fluid Mech., 44 (1970), pp. 791-810.
34. K. L. BILLIAR and M. S. SACKS, Biaxial mechanical properties of the native and glutaraldehyde treated aortic valve cusp: Part II-A structural constitutive model, J. Biomech. Eng., 122 (2000), pp. 327-335.
35. D. M. KNAPP, V. H. BAROCAS, A. MOON, K. YOO, L. R. PETZOLD, and R. T. TRANQUILLO, Rheology of reconstituted type I collagen gel in confined compression, J. Rheology, 41 (1997), pp. 971-993.
36. T. T. TOWER, M. R. NEIDERT, and R. T. TRANQUILLO, Fiber alignment imaging during mechanical testing of soft tissues, Ann. Biomed. Eng., 30 (2002), pp. 1221-1233.
37. M. A. SOLTZ and G. A. ATESHIAN, A conewise linear elasticity mixture model for the analysis of tension-compression nonlinearity in articular cartilage, J. Biomech. Eng., 122 (2000), pp. 576-586.
38. G. A. ATESHIAN, M. A. SOLTZ, R. L. MAUCK, I. N. BASALO, C. T. HUNG, and W. M. LAI, The role of osmotic pressure and tension-compression nonlinearity in the frictional response of articular cartilage, Transp. Porous Media, 50 (2003), pp. 5-33.
39. W. M. LAI, J. S. HOU, and V. C. MOW, A triphasic theory for the swelling and deformation behaviors of articular cartilage, J. Biomech. Eng., 113 (1991), pp. 245-258.
40. W. Y. GU, H. YAO, C. Y. HUANG, and H. S. CHEUNG, New insight into defrmation-dependent hydraulic permeability of gels and cartilage, and dynamic behavior of agarose gels in confined compression, J. Biomechanics, 36 (2003), pp. 593-598.
41. T. STYLIANOPOULOS, A. YECKEL, J. J. DERBY, X. LUO, M. S. SHEPHARD, E. SANDER, and V. H. BAROCAS, Permeability calculations in three-dimensional isotropic and oriented fiber networks, J. Phys. Fluids, in preparation.
42. X. LUO, T. STYLIANOPOULOS, V. H. BAROCAS, and M. S. SHEPARD, Multiscale computation for soft tissues with complex geometries, J. Engineering with Computers, to appear.