Solute transport across a contact interface in deformable porous media

Journal of Biomechanics

Volumn 45, Issue 6, 2012, Pages 1023-1027

  Ateshian, Gerard A ^a   Maas, Steve ^b   Weiss, Jeffrey A ^b  

^a Columbia University ^*  (United States)

^b UNIVERSITY OF UTAH   (United States)

Author keywords

Biphasic theory; Contact mechanics; Finite element modeling; Porous media; Solute transport

Indexed keywords

ANALYTICAL SOLUTIONS; BIPHASIC THEORY; CONTACT ALGORITHMS; CONTACT INTERFACE; CONTACT MECHANICS; CONTACTING SURFACES; DEFORMABLE POROUS MEDIA; FINITE ELEMENT CODES; FINITE ELEMENT FORMULATIONS; FINITE ELEMENT MODELING; MECHANOCHEMICALS; MOLAR FLUX; OPEN-SOURCE; PENALTY METHODS; PUBLIC DOMAINS; SOLUTE CONCENTRATIONS; VIRTUAL WORKS;

ALGORITHMS; BIOMECHANICS; DEFORMATION; POROUS MATERIALS; TISSUE;

SOLUTE TRANSPORT;

ALGORITHM; ARTICLE; BIOMECHANICS; CONCENTRATION (PARAMETERS); DIFFUSION; FLUID TRANSPORT; MUSCLE METABOLISM; PRIORITY JOURNAL; SOLUTE; STATISTICAL ANALYSIS; STEADY STATE; THERMODYNAMICS; TRANSPORT MEDIUM; VALIDATION PROCESS;

ALGORITHMS; ANIMALS; BIOLOGICAL TRANSPORT; FINITE ELEMENT ANALYSIS; HUMANS; MODELS, BIOLOGICAL; POROSITY;

EID: 84858615196     PISSN: 00219290     EISSN: 18732380     Source Type: Journal    
DOI: 10.1016/j.jbiomech.2012.01.003     Document Type: Article

References (21)

1. Ateshian G.A. On the theory of reactive mixtures for modeling biological growth. Biomechanics and Modeling in Mechanobiology 2007, 6(6):423-445.
2. Ateshian, G.A., Albro, M.B., Maas, S., Weiss, J.A., 2011. Finite element implementation of mechano-chemical phenomena in neutral deformable porous media under finite deformation. Journal of Biomechanical Engineering, in press. http://10.1115/1.4005694.
3. Ateshian G.A., Maas S., Weiss J.A. Finite element algorithm for frictionless contact of porous permeable media under finite deformation and sliding. Journal of Biomechanical Engineering 2010, 132(6):061006.
4. Bonet J., Wood R.D. Nonlinear Continuum Mechanics for Finite Element Analysis 1997, Cambridge University Press, Cambridge, New York, NY.
5. Bowen R. Incompressible porous media models by use of the theory of mixtures. International Journal of Engineering Science UK 1980, 18(9):1129-1148.
6. Crank J. The Mathematics of Diffusion 1979, Clarendon Press, Oxford, England. 2nd ed.
7. Donzelli P.S., Spilker R.L., Ateshian G.A., Mow V.C. Contact analysis of biphasic transversely isotropic cartilage layers and correlations with tissue failure. Journal of Biomechanics 1999, 32(10):1037-1047.
8. Eringen A., Ingram J. Continuum theory of chemically reacting media-1. International Journal of Engineering Science 1965, 3:197-212.
9. Frijns A.J.H., Huyghe J.M., Janssen J.D. Validation of the quadriphasic mixture theory for intervertebral disc tissue. International Journal of Engineering Science 1997, 35(15):1419-1429.
10. Kaasschieter E.F., Frijns A.J.H., Huyghe J.M. Mixed finite element modelling of cartilaginous tissues. Mathematics and Computers in Simulation 2003, 61(3-6):549-560.
11. Lai W.M., Hou J.S., Mow V.C. A triphasic theory for the swelling and deformation behaviors of articular cartilage. Journal of Biomechanical Engineering 1991, 113(3):245-258.
12. Laursen T., Simo J. A continuum-based finite element formulation for the implicit solution of multibody, large deformation frictional contact problems. International Journal for Numerical Methods in Engineering (UK) 1993, 36(20):3451-3586.
13. Mauck R.L., Hung C.T., Ateshian G.A. Modeling of neutral solute transport in a dynamically loaded porous permeable gel: implications for articular cartilage biosynthesis and tissue engineering. Journal of Biomechanical Engineering 2003, 125(5):602-614.
14. Mow V.C., Kuei S.C., Lai W.M., Armstrong C.G. Biphasic creep and stress relaxation of articular cartilage in compression? Theory and experiments. Journal of Biomechanical Engineering 1980, 102(1):73-84.
15. Sengers B.G., Oomens C.W., Baaijens F.P. An integrated finite-element approach to mechanics, transport and biosynthesis in tissue engineering. Journal of Biomechanical Engineering 2004, 126(1):82-91.
16. Simon B.R., Liable J.P., Pflaster D., Yuan Y., Krag M.H. A poroelastic finite element formulation including transport and swelling in soft tissue structures. Journal of Biomechanical Engineering 1996, 118(1):1-9.
17. Steck R., Niederer P., Knothe Tate M.L. A finite element analysis for the prediction of load-induced fluid flow and mechanochemical transduction in bone. Journal of Theoretical Biology 2003, 220(2):249-259.
18. Sun D.N., Gu W.Y., Guo X.E., Lai W.M., Mow V.C. A mixed finite element formulation of triphasic mechano-electrochemical theory for charged, hydrated biological soft tissues. International Journal for Numerical Methods in Engineering 1999, 45(10):1375-1402.
19. Un K., Spilker R.L. A penetration-based finite element method for hyperelastic 3D biphasic tissues in contact. Part II. Finite element simulations. Journal of Biomechanical Engineering 2006, 128(6):934-942.
20. Yang T., Spilker R.L. A Lagrange multiplier mixed finite element formulation for three-dimensional contact of biphasic tissues. Journal of Biomechanical Engineering 2007, 129(3):457-471.
21. Yao H., Gu W.Y. Three-dimensional inhomogeneous triphasic finite-element analysis of physical signals and solute transport in human intervertebral disc under axial compression. Journal of Biomechanics 2007, 40(9):2071-2077.