A linearized formulation of triphasic mixture theory for articular cartilage, and its application to indentation analysis

Journal of Biomechanics

Volumn 43, Issue 4, 2010, Pages 673-679

  Lu, Xin L ^a   Wan, Leo Q ^a   Edward Guo, X ^a   Mow, Van C ^a  

^a Columbia University ^*  (United States)

Author keywords

Aspect Ratio; Indentation Creep; Linearization; Osmotic Pressure; Proteoglycan; Stress Relaxation

Indexed keywords

ARTICULAR CARTILAGES; AXISYMMETRIC PROBLEMS; CARTILAGE REPAIR; CARTILAGE THICKNESS; CHONDROCYTES; COMPLICATED LOADINGS; ENGINEERING DESIGN; FINITE DIFFERENCE; FLOW BEHAVIORS; FLUID PRESSURES; GOVERNING EQUATIONS; IN-VIVO; INDENTATION ANALYSIS; INDENTATION CREEP; INDENTATION EXPERIMENT; INDENTERS; MATHEMATICAL COMPLEXITY; MECHANICAL BEHAVIOR; MECHANOTRANSDUCTION; MIXTURE THEORY; NEGATIVE CHARGE; NUMERICAL PROGRAMS; PERTURBATION METHOD; POTENTIAL FUNCTION; PROTEOGLYCANS; SOFT TISSUE; SOLID MATRIXES; TISSUE RESPONSE; UNCONFINED COMPRESSION; VISCOUS EFFECT;

ASPECT RATIO; CHEMICAL PROPERTIES; FLUID DYNAMICS; GLYCOPROTEINS; INDENTATION; LINEARIZATION; LOADING; MIXTURES; OSMOSIS; STIFFNESS MATRIX; STRESS RELAXATION; TISSUE; TISSUE ENGINEERING;

CARTILAGE;

PROTEOGLYCAN;

ARTICLE; ARTICULAR CARTILAGE; BIOMECHANICS; COMPRESSION; ELECTROCHEMISTRY; FLUID FLOW; FLUID PRESSURE; HYDRAULIC PERFUSION; INDENTATION ANALYSIS; MATHEMATICAL ANALYSIS; MECHANICAL STRESS; PHYSICAL PARAMETERS; PRIORITY JOURNAL; RIGIDITY; THEORY; TRIPHASIC MIXTURE THEORY; BIOLOGICAL MODEL; COMPUTER SIMULATION; HARDNESS; HUMAN; METHODOLOGY; PHYSIOLOGY; STATIC ELECTRICITY; STATISTICAL MODEL; VISCOSITY; YOUNG MODULUS;

CARTILAGE, ARTICULAR; COMPUTER SIMULATION; ELASTIC MODULUS; HARDNESS; HARDNESS TESTS; HUMANS; LINEAR MODELS; MODELS, BIOLOGICAL; PROTEOGLYCANS; STATIC ELECTRICITY; STRESS, MECHANICAL; VISCOSITY;

EID: 77952516400     PISSN: 00219290     EISSN: 18732380     Source Type: Journal    
DOI: 10.1016/j.jbiomech.2009.10.026     Document Type: Article

References (28)

1. Athanasiou K.A., Rosenwasser M.P., Buckwalter J.A., Malinin T.I., Mow V.C. Interspecies comparisons of in situ intrinsic mechanical properties of distal femoral cartilage. Journal of Orthopaedic Research 1991, 9:330-340.
2. Bae W.C., Law A.W., Amiel D., Sah R.L. Sensitivity of indentation testing to step-off edges and interface integrity in cartilage repair. Annals of Biomedical Engineering 2004, 32:360-369.
3. Bae W.C., Lewis C.W., Levenston M.E., Sah R.L. Indentation testing of human articular cartilage: effects of probe tip geometry and indentation depth on intra-tissue strain. Journal of Biomechanics 2006, 39:1039-1047.
4. Donnan F.G. The theory of membrane equilibria. Chemical Reviews 1924, 1:73-90.
5. Flahiff C.M., Narmoneva D.A., Huebner J.L., Kraus V.B., Guilak F., Setton L.A. Osmotic loading to determine the intrinsic material properties of guinea pig knee cartilage. Journal of Biomechanics 2002, 35:1285-1290.
6. Frank E.H., Grodzinsky A.J. Cartilage electromechanics-II. A continuum model of cartilage electrokinetics and correlation with experiments. Journal of Biomechanics 1987, 20:629-639.
7. Gu W.Y., Lai W.M., Mow V.C. A mixture theory for charged-hydrated soft tissues containing multi-electrolytes: passive transport and swelling behaviors. Journal of Biomechanical Engineering 1998, 120:169-180.
8. Hayes W.C., Keer L.M., Herrmann G., Mockros L.F. A mathematical analysis for indentation tests of articular cartilage. Journal of Biomechanics 1972, 5:541-551.
9. Holmes M.H., Lai W.M., Mow V.C. Singular perturbation analysis of the nonlinear, flow-dependent compressive stress relaxation behavior of articular cartilage. Journal of Biomechanical Engineering 1985, 107:206-218.
10. Huang C.Y., Stankiewicz A., Ateshian G.A., Mow V.C. Anisotropy, inhomogeneity, and tension-compression nonlinearity of human glenohumeral cartilage in finite deformation. Journal of Biomechanics 2005, 38:799-809.
11. Julkunen P., Korhonen R.K., Herzog W., Jurvelin J.S. Uncertainties in indentation testing of articular cartilage: a fibril-reinforced poroviscoelastic study. Medical Engineering & Physics 2007, 30:506-515.
12. 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, 113:245-258.
13. Lai W.M., Mow V.C., Sun D.D., Ateshian G.A. On the electric potentials inside a charged soft hydrated biological tissue: streaming potential versus diffusion potential. Journal of Biomechanical Engineering 2000, 122:336-346.
14. Lu X.L., Miller C., Chen F.H., Guo X.E., Mow V.C. The generalized triphasic correspondence principle for simultaneous determination of the mechanical properties and proteoglycan content of articular cartilage by indentation. Journal of Biomechanics 2007, 40:2434-2441.
15. Lu X.L., Mow V.C., Guo X.E. Proteoglycans and mechanical behavior of condylar cartilage. Journal of Dental Research 2009, 88:244-248.
16. Lu X.L., Sun D.D., Guo X.E., Chen F.H., Lai W.M., Mow V.C. Indentation determined mechanoelectrochemical properties and fixed charge density of articular cartilage. Annals of Biomedical Engineering 2004, 32:370-379.
17. Mak A.F., Lai W.M., Mow V.C. Biphasic indentation of articular cartilage-I. Theoretical analysis. Journal of Biomechanics 1987, 20:703-714.
18. Maroudas A.I. Balance between swelling pressure and collagen tension in normal and degenerate cartilage. Nature 1976, 260:808-809.
19. Mow V.C., Gibbs M.C., Lai W.M., Zhu W.B., Athanasiou K.A. Biphasic indentation of articular cartilage-II. A numerical algorithm and an experimental study. Journal of Biomechanics 1989, 22:853-861.
20. Mow V.C., Gu W.Y., Chen F.H. Structure and function of articular cartilage and meniscus. Basic Orthopaedic Biomechanics and Mechano-biology 2005, 181-258. Lippincott Williams & Wilkins, Philadelphia. V.C. Mow, R. Huiskes (Eds.).
21. 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, 102:73-84.
22. Narmoneva D.A., Wang J.Y., Setton L.A. A noncontacting method for material property determination for articular cartilage from osmotic loading. Biophysical Journal 2001, 81:3066-3076.
23. Neuber H. On a new attempt at solving the spatial problem of elasticity theories-Hollow cones under concentrad loads as an example. Zeitschrift Fur Angewandte Mathematik Und Mechanik 1934, 14:203-212.
24. Schiesser W.E. The Numerical Method of Lines 1991, Academic Press, San Diego.
25. Sokoloff L. Elasticity of aging cartilage. Federation Proceedings 1966, 25:1089-1095.
26. Spilker R.L., Suh J.K., Mow V.C. A finite element analysis of the indentation stress-relaxation response of linear biphasic articular cartilage. Journal of Biomechanical Engineering 1992, 114:191-201.
27. Sweigart M.A., Athanasiou K.A. Biomechanical characteristics of the normal medial and lateral porcine knee menisci. Proceedings of the Institution of Mechanical Engineers H 2005, 219:53-62.
28. Yao H., Gu W.Y. Convection and diffusion in charged hydrated soft tissues: a mixture theory approach. Biomechanics and Modeling in Mechanobiology 2007, 6:63-72.