Computational aspects in mechanical modeling of the articular cartilage tissue

Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine

Volumn 227, Issue 4, 2013, Pages 402-420

  Mohammadi, Hadi ^a   Mequanint, Kibret ^b   Herzog, Walter ^c  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

^b UNIVERSITY OF WESTERN ONTARIO   (Canada)

^c UNIVERSITY OF CALGARY   (Canada)

Author keywords

Articular cartilage; Cartilage mechanics; Chondrocyte mechanobiology; Computational mechanics; Continuum model; Finite element method; Large deformation theory; Numerical modeling

Indexed keywords

ARTICULAR CARTILAGES; CARTILAGE MECHANICS; CONTINUUM MODEL; LARGE DEFORMATION THEORIES; MECHANO-BIOLOGY; CONTINUUM MODELING;

BODY FLUIDS; COMPUTATIONAL MECHANICS; CONTINUUM MECHANICS; FINITE ELEMENT METHOD; NUMERICAL MODELS; TISSUE; CARTILAGE; COMPUTATION THEORY; MECHANICS; NUMERICAL METHODS; TISSUE ENGINEERING;

CARTILAGE; FINITE ELEMENT METHOD;

BIOMATERIAL; CHONDROITIN SULFATE; KERATAN SULFATE;

ANIMAL; ARTICULAR CARTILAGE; BIOLOGICAL MODEL; CARTILAGE; CARTILAGE CELL; CARTILAGE MECHANICS; CHEMISTRY; CHONDROCYTE MECHANOBIOLOGY; COMPRESSIVE STRENGTH; COMPUTATIONAL MECHANICS; COMPUTER SIMULATION; CONTINUUM MODEL; CYTOLOGY; FINITE ELEMENT ANALYSIS; FINITE ELEMENT METHOD; HUMAN; KNEE; LARGE DEFORMATION THEORY; MECHANICAL STRESS; NUMERICAL MODELING; PATHOLOGY; POROSITY; REVIEW; STATISTICAL MODEL; SURFACE PROPERTY; THEORETICAL MODEL;

ARTICULAR CARTILAGE; CARTILAGE MECHANICS; CHONDROCYTE MECHANOBIOLOGY; COMPUTATIONAL MECHANICS; CONTINUUM MODEL; FINITE ELEMENT METHOD; LARGE DEFORMATION THEORY; NUMERICAL MODELING;

ANIMALS; BIOCOMPATIBLE MATERIALS; CARTILAGE; CARTILAGE, ARTICULAR; CHONDROCYTES; CHONDROITIN SULFATES; COMPRESSIVE STRENGTH; COMPUTER SIMULATION; FINITE ELEMENT ANALYSIS; HUMANS; KERATAN SULFATE; KNEE JOINT; MODELS, BIOLOGICAL; MODELS, STATISTICAL; MODELS, THEORETICAL; POROSITY; STRESS, MECHANICAL; SURFACE PROPERTIES;

MLCS; MLOWN;

EID: 84877835750     PISSN: 09544119     EISSN: 20413033     Source Type: Journal    
DOI: 10.1177/0954411912470239     Document Type: Review

References (177)

1. Hynes RO. Integrins: versatility, modulation, and signaling in cell adhesion. Cell 1992; 69: 11-25.
2. Shyy JYJ and Chien S. Role of integrins in cellular response to mechanical stress and adhesion. Curr Opin Cell Biol 1997; 9: 707-713.
3. Mow VC, Gu WY and Chen FH. Structure and function of articular cartilage and meniscus. In: Mow VC and Huiskes R (eds) Basic orthopaedic biomechanics and mechano-biology. Philadelphia, PA, USA, Lippincott Williams & Wilkins, 2005, pp.181-258.
4. Andrews S, Shrive N and Ronsky J. The shocking truth about meniscus. J Biomech 2011; 44(16): 2737-2740.
5. Mow VC, Proctor CS and Kelly MA. Biomechanics of articular cartilage. In: Nordin M and Frankel VH (eds) Basic biomechanics of the mucoskeletal system, 2nd ed. Philadelphia, PA: Lea & Febiger, 1989, pp.31-57.
6. Stockwell RA. Biology of cartilage cells. Cambridge: Cambridge University Press, 1979.
7. Mizrahi J, Maroudas A, Lanir Y, et al. The instantaneous deformation of cartilage: effects of collagen fire orientation and osmotic stress. Biorheology 1986; 23: 311-330.
8. Palmoski M and Brandt K. Effects of static and cyclic compressive loading on articular cartilage plugs in vitro. Arthritis Rheum 1984; 27: 675-681.
9. Guilak F. Compression-induced changes in the shape and volume of the chondrocyte nucleus. J Biomech 1995; 28: 1529-1541.
10. Buschmann MD, Hunziker EB, Kim YJ, et al. Altered aggrecan synthesis correlates with cell and nucleus structure in statically compressed cartilage. J Cell Sci 1996; 109: 499-508.
11. Wong M, Wuethrich P, Buschmann MD, et al. Chondrocyte biosynthesis correlates with local tissue strain in statically compressed adult articular cartilage. J Orthop Res 1997; 15: 189-196.
12. Quinn TM, Grodzinsky AJ, Buschmann MD, et al. Mechanical compression alters proteoglycan deposition and matrix deformation around individual cells in cartilage explants. J Cell Sci 1998; 111: 573-583.
13. Freeman PM, Natarajan RN, Kimura JH, et al. Chondrocyte cells respond mechanically to compressive loads. J Orthop Res 1994; 12: 311-320.
14. Lee DA, Knight MM, Bolton JF, et al. Chondrocyte deformation within compressed agarose constructs at the cellular and sub-cellular levels. J Biomech 2000; 33: 81-95.
15. Kim YJ, Sah RY, Grodzinsky AJ, et al. Mechanical regulation of cartilage biosynthetic behaviour: physical stimuli. Arch Biochem Biophys 1994; 311: 1-12.
16. Choi JB, Youn I, Cao L, et al. Zonal changes in the three-dimensional morphology of the chondron under compression: the relationship among cellular, pericellular, and extracellular deformation in articular cartilage. J Biomech 2007; 40: 2596-2603.
17. Clark AL, Barclay LD, Matyas JR, et al. In situ chondrocyte deformation with physiological compression of the feline patellofemoral joint. J Biomech 2003; 36: 553-568.
18. Craig S. Effects of in-vivo joint loading on articular cartilage chondrocyte viability. Master's Thesis, University of Calgary, Canada, 2003.
19. Clark AL, Leonard B, Barclay BA, et al. Opposing cartilages in the patellofemoral joint adapt differently to longterm cruciate deficiency: chondrocyte deformation and reorientation with compression. Osteoarthr Cartil 2005; 13: 1100-1114.
20. Clark AL, Leonard B, Barclay BA, et al. Heterogeneity in patellofemoral cartilage adaptation to anterior cruciate ligament transaction; chondrocyte shape and deformation with compression. Osteoarthr Cartil 2006; 14: 120-130.
21. Mow VA and Guo E Mechano-electrochemical properties of articular cartilage: their in-homogeneities and anisotropies. Annu Rev Biomed Eng 2002; 4: 175-209.
22. Alford JW and Cole BJ. Cartilage restoration, part 1: basic science, historical perspective, patient evaluation, and treatment options. Am J Sports Med 2005; 33(2): 295-306.
23. Poole CA, Flint M and Beaumont BW. Chondrons in cartilage: ultrastructural analysis of the pericellular microenvironment in adult human articular cartilages. J Orthop Res 1987; 6: 509-522.
24. Knight MM, Ross JM, Sherwin AF, et al. Chondrocyte deformation within mechanically and enzymatically extracted chondrons compressed in agarose. Biochim Biophys Acta 2001; 1526: 141-146.
25. Youn I, Choi JB, Cao L, et al. Zonal variations in the three-dimensional morphology of the chondron measured in situ using confocal microscopy. Osteoarthr Cartil 2006; 14: 889-897.
26. Koelling S, Clauditz TS, Kaste M, et al. Cartilage oligomeric matrix protein is involved in human limb development and in the pathogenesis of osteoarthritis. Arthritis Res Ther 2006; 8(3): R56.
27. Jones WR, Ting-Beall HP, Lee GM, et al. Alterations in the Young's modulus and volumetric properties of chondrocytes isolated from normal and osteoarthritic human cartilage. J Biomech 1999; 32: 119-127.
28. Schinagl RM, Gurskis D, Chen AC, et al. Depth-dependent confined compression modulus of full-thickness bovine articular cartilage. J Orthop Res 1997; 15: 499-506.
29. Guilak F, Ratclilffe A and Mow VC. Chondrocyte deformation and local tissue strain in articular cartilage: a confocal microscopy study. J Orthop Res 1995; 13: 410-421.
30. Han SK and Herzog W. Mechanical loading of in-situ chondrocytes in their native environment. In: Proceedings of the North American Congress on biomechanics, Ann Arbor, MI, USA, 5-9 August 2008.
31. Guilak F and Mow VC. The mechanical environment of the chondrocyte: a biphasic finite element model of cellmatrix interactions in articular cartilage. J Biomech 2000; 33: 1663-1673.
32. Alexopoulos LG, Setton LA and Guilak F. The biomechanical role of the chondrocyte pericellular matrix in articular cartilage. Acta Biomater 2005; 1: 317-325.
33. Korhonen RK and Herzog W. Depth-dependent analysis of the role of collagen fibrils, fixed charges and fluid in the pericellular matrix of articular cartilage on chondrocyte mechanics. J Biomech 2008; 41: 480-485.
34. Mak AF. The apparent viscoelastic behavior of articular cartilage - the contributions from the intrinsic matrix viscoelasticity and interstitial fluid flows. J Biomech Eng 1986; 108(2): 123-130.
35. Mak AF. Unconfined compression of hydrated viscoelastic tissues: a biphasic poroviscoelastic analysis. Biorheology 1986; 23(4): 371-383.
36. Suh JK and Bai S. Finite element formulation of biphasic poroviscoelastic model for articular cartilage. J Biomech Eng 1998; 120(2): 195-201.
37. Betsch DF and Baer E. Structure and mechanical properties of rat-tail tendon. Biorheology 1980; 17: 83-94.
38. Haut RC. Age-dependent influence of strain rate on the tensile failure of rat-tail tendon. J Biomech Eng 1983; 105: 296-299.
39. Silver FH, Ebrahimi A and Snowhill PB. Viscoelastic properties of self-assembled type I collagen fibers: molecular basis of elastic and viscous behaviors. Connect Tissue Res 2002; 43: 569-580.
40. Viidik Q. A rheological model for uncalcified parallelfibriled collagenous soft tissue. J Biomech 1968; 1: 3-11.
41. Wang JL, Parnianpour M, Shirazi-Adl A, et al. Failure criterion of collagen fiber: viscoelastic behavior simulated by using load control data. Theor Appl Fract Mec 1997; 27: 1-12.
42. Haut RC and Little RW. A constitutive equation for collagen fibers. J Biomech 1972; 5: 423-430.
43. Sanjeevi R, Somanathan N and Ramaswamy D. A viscoelastic model for collagen fibres. J Biomech 1982; 15: 181-183.
44. Mow VC, Holmes MH and Lai WM. Fluid transport and mechanical properties of articular cartilage: a review. J Biomech 1984; 17(5): 377-394.
45. Mow VC, Mak AF, Lai WM, et al. Viscoelastic properties of proteoglycan subunits and aggregates in varying solution concentrations. J Biomech 1984; 17(5): 325-338.
46. Zhu W, Mow VC, Koob TJ, et al. Viscoelastic shear properties of articular cartilage and the effects of glycosidase treatments. J Orthop Res 1993; 11(6): 771-781.
47. Maroudas A. Physicochemical properties of articular cartilage. In: Freeman MAR (ed.) Adult articular cartilage, 2nd ed. Kent: Pitman Medical, 1979, pp.215-323.
48. Urban JPG, Maroudas A, Bayliss MT, et al. Swelling pressures of PG's at the concentrations found in cartilaginous tissues. Biorheology 1979; 16: 447-464.
49. Mow VC, Kuei SC, Lai WM, et al. Biphasic creep and stress relaxation of articular cartilage in compression: theory and experiments. J Biomech Eng 1980; 102: 73-84.
50. Lai WM and Mow VC. Drag-induced compression of articular cartilage during a permeation experiment. Biorheology 1980; 17: 111-123.
51. Gu WY, Lai WM and Mow VC. Transport of fluid and ions through a porous-permeable charged-hydrated tissue, and streaming potential data on normal bovine articular cartilage. J Biomech 1993; 26: 709-723.
52. Gu WY, Lai WM and Mow VC. A mixture theory for charged-hydrated soft tissues containing multi-electrolytes: passive transport and swelling behaviors. J Biomech Eng 1998; 120: 169-180.
53. Maroudas A. Transport of solutes through cartilage: permeability to large molecules. J Anat 1976; 122: 335-347.
54. Lai WM, Hou JS and Mow VC. A triphasic theory for the swelling and deformation behaviours of articular cartilage. J Biomech Eng 1991; 113: 245-258.
55. Bader DL, Kempson GE, Egan J, et al. The effects of selective matrix degradation on the short-term compressive properties of adult human articular cartilage. Biochim Biophys Acta 1992; 1116(2): 147-154.
56. Herzog W, Diet S, Suter E, et al. Material and functional properties of articular cartilage and patellofemoral contact mechanics in an experimental model of osteoarthritis. J Biomech 1998; 31: 1137-1145.
57. Mow VC and Ratcliffe A. Structure and function of articular cartilage and meniscus. In: Mow VC and Hayes WC (eds) Basic orthopaedic biomechanics, 2nd ed. Philadelphia, PA: Lippincott-Raven, pp.113-177.
58. Holmes MH and Mow VC. The nonlinear characteristics of soft gels and hydrated connective tissues in ultrafiltration. J Biomech 1990; 23: 1145-1156.
59. Soltz MA and Ateshian GA. Experimental verification and theoretical prediction of cartilage interstitial fluid pressurization at an impermeable contact interface in confined compression. J Biomech 1998; 31: 927-934.
60. Setton LA, Zhu W and Mow VC. The biphasic poroviscoelastic behaviour of articular cartilage: role of the surface zone in governing the compressive behavior. J Biomech 1993; 26(4/5): 581-592.
61. Mohammadi H, Mequanint K and Herzog W. A p-type finite element solution for the simulation of O2 transport in articular cartilage tissue: heterogeneous and porous media. Proc IMechE, Part H: J Engineering in Medicine 2011; 225(10): 1003-1014.
62. Akizuki S, Mow VC, Muller F, et al. Tensile properties of human knee joint cartilage: I. Influence of ionic conditions, weight bearing, and fibrillation on the tensile modulus. J Orthop Res 1986; 4(4): 379-392.
63. Roth V and Mow VC. The intrinsic tensile behavior of the matrix of bovine articular cartilage and its variation with age. J Bone Joint Surg 1980; 62: 1102-1117.
64. Woo SY, Akeson WH and Jemmott GF. Measurements of nonhomogeneous directional mechanical properties of articular cartilage in tension. J Biomech 1976; 9: 785-791.
65. Hayes WC and Bodine AJ. Flow-independent viscoelastic properties of articular cartilage matrix. J Biomech 1978; 11(8-9): 407-419.
66. Spirt AA, Mak AF and Wassell RP. Nonlinear viscoelastic properties of articular cartilage in shear. J Orthop Res 1989; 7(1): 43-49.
67. Mansour JM. Biomechanics of cartilage. In: Oatis CA (ed.) Kinesiology: the mechanics and pathomechanics of human movement. Philadelphia, PA: Lippincott Williams & Wilkins, 2003, ch. 5, pp.66-79.
68. Simon BR, Liable JP, Pflaster D, et al. A poroelastic finite element formulation including transport and swelling in soft tissue structures. J Biomech Eng 1996; 118: 1-9.
69. Huyghe JM and Janssen JD. Quadriphasic theory of swelling incompressible porous media. Int J Eng Sci 1997; 35: 793-802.
70. Maroudas A. Physicochemical properties of cartilage in the light of ion exchange theory. Biophys J 1968; 8(5): 575-595.
71. Mankin HJ, Mow VC, Buckwalter JA, et al. Articular cartilage structure, composition, and function. In: Buckwalter JA, Einhorn TA and Simon SR (eds) Orthopaedic basic science: biology and biomechanics of the musculoskeletal system. Rosemont, IL: American Academy of Orthopaedic Surgeons Publishers, 2000, pp.47-92.
72. Linn FC. Lubrication of animal joints. I. The arthrotripsometer. J Bone Joint Surg 1967; 49: 1079-1098.
73. McCutchen C. Mechanism of animal joints. Nature 1959; 184: 1284-1285.
74. Unsworth A, Dowson D and Wright V. The frictional behaviour of human synovial joints. I, natural joints. J Lubr Technol 1975; 97: 369-376.
75. Linn FC and Sokoloff L. Movement and composition of interstitial fluid of cartilage. Arthritis Rheum 1965; 8: 481-494.
76. Radin EL and Paul IL. A consolidated concept of joint lubrication. J Bone Joint Surg 1972; 54: 607-616.
77. Radin EL, Paul IL and Pollock D. Animal joint behavior under excessive loading. Nature 1970; 226: 554-555.
78. Swann DA, Hendren RB and Radin EL. The lubricating activity of synovial fluid glycoproteins. Arthritis Rheum 1981; 24: 22-30.
79. Noyori K, Takagi T and Jasin HE. Characterization of the macromolecular components of the articular cartilage surface. Rheumatol Int 1998; 18: 71-77.
80. Schumacher BL, Block JA, Schmid TM, et al. A novel proteoglycan synthesized and secreted by chondrocytes of the superficial zone of articular cartilage. Arch Biochem Biophys 1994; 311: 144-152.
81. Jay GD. Lubricin and surfacing of articular joints. Curr Opin Orthop 2004; 15: 355-359.
82. Sarma AV, Powell GL and LaBerge M. Phospholipid composition of articular cartilage boundary lubricant. J Orthop Res 2001; 19: 671-676.
83. Schmidt TA and Sah RL. Effect of synovial fluid on boundary lubrication of articular cartilage. Osteoarthr Cartil 2007; 15: 35-47.
84. Davis WH, Lee SL and Sokoloff L. A proposed model of boundary lubrication by synovial fluid: structure of boundary water. J Biomech Eng 1979; 101: 185-192.
85. Malcom LL. An experimental investigation of the frictional and deformational responses of articular cartilage interfaces to static and dynamic loading. Dissertation, University of California San Diego, San Diego, CA, 1976.
86. Jones ES. Joint lubrication. Lancet 1934; 223: 1426-1427.
87. Charnley J. Lubrication of animal joints. In: Proceedings of the symposium on biomechanics, 1959, pp.12-22. London: Institute of Mechanical Engineers.
88. Jay GD, Haberstroh K and Cha CJ. Comparison of the boundary lubricating ability of bovine synovial fluid, lubricin, and Healon. J Biomed Mater Res 1998; 40: 414-418.
89. Jay GD and Cha CJ. The effect of phospholipase digestion upon the boundary lubricating activity of synovial fluid. J Rheumatol 1999; 26: 2454-2457.
90. Mabuchi K, Obara T, Ikegami K, et al. Molecular weight independence of the effect of additive hyaluronic acid on the lubricating characteristics in synovial joints with experimental deterioration. Clin Biomech (Bristol, Avon) 1999; 14: 352-356.
91. Radin EL, Swann DA and Weisser PA. Separation of a hyaluronatefree lubricating fraction from synovial fluid. Nature 1970; 228: 377-378.
92. Bell CJ, Ingham E and Fisher J. Influence of hyaluronic acid on the time-dependent friction response of articular cartilage under different conditions. Proc IMechE, Part H: J Engineering in Medicine 2006; 220: 23-31.
93. Linn FC. Lubrication of animal joints. II. The mechanism. J Biomech 1968; 1: 193-205.
94. Higaki H, Murakami T, Nakanishi Y, et al. The lubricating ability of biomembrane models with dipalmitoyl phosphatidylcholine and gamma-globulin. Proc IMechE, Part H: J Engineering in Medicine 1998; 212: 337-346.
95. Murakami T, Higaki H, Sawae Y, et al. Adaptive and multimode lubrication in natural synovial joints and artificial joints. Proc IMechE, Part H: J Engineering in Medicine 1998; 212: 23-35.
96. Kumar P, Oka M, Toguchida J, et al. Role of uppermost superficial surface layer of articular cartilage in the lubrication mechanism of joints. J Anat 2001; 199: 241-250.
97. Jay GD, Lane BP and Sokoloff L. Characterization of a bovine synovial fluid lubricating factor. III. The interaction with hyaluronic acid. Connect Tissue Res 1992; 28: 245-255.
98. Ikegawa S, Sano M, Koshizuka Y, et al. Isolation, characterization and mapping of the mouse and human PRG4 (proteoglycans 4) genes. Cytogenet Cell Genet 2000; 90: 291-297.
99. Jay GD. Characterization of a bovine synovial fluid lubricating factor. I. Chemical, surface activity and lubricating properties. Connect Tissue Res 1992; 28: 71-88.
100. Jay GD, Tantravahi U, Britt DE, et al. Homology of lubricin and superficial zone protein (SZP): products of megakaryocyte stimulating factor (MSF) gene expression by human synovial fibroblasts and articular chondrocytes localized to chromosome 1q25. J Orthop Res 2001; 19: 677-687.
101. Ozturk HE, Stoffel K, Jones CF, et al. The effect of surface-active phospholipids on the lubrication of osteoarthritic sheep knee joints: friction. Tribol Lett 2004; 16: 283-289.
102. Walker PS and Erkman MJ. The role of the menisci in force transmission across the knee. Clin Orthop Relat Res 1975; 109: 184-192.
103. Walker PS, Sikorski J and Dowson D. Features of the synovial fluid film in human joint lubrication. Nature 1970; 225: 956-957.
104. Hou JS, Holmes MH, Lai WM, et al. Boundary conditions at the cartilage-synovial fluid interface for joint lubrication and theoretical verifications. J Biomech Eng 1989; 111: 78-87.
105. Hou JS, Mow VC, Lai WM, et al. An analysis of the squeeze-film lubrication mechanism for articular cartilage. J Biomech 1992; 25: 247-259.
106. Jin ZM, Dowson D and Fisher J. Effect of porosity of articular cartilage on the lubrication of a normal human hip joint. Proc IMechE, Part H: J Engineering in Medicine 1992; 206: 117-124.
107. Biot MA. General theory of three-dimensional consolidation. J Appl Phys 1941; 12: 155-164.
108. Levenston ME, Frank EH and Zrodzinsky AJ. Variationally derived 3-field finite element formulations for quasistatic poroelastic analysis of hydrated biological tissues. Comput Methods Appl Mech Eng 1998; 156: 231-246.
109. Armstrong CG and Mow VC. Variations in the intrinsic mechanical properties of human articular cartilage with age, degeneration, and water content. J Bone Joint Surg 1982; 64: 88-94.
110. Guilak F, Ratcliffe A, Lane N, et al. Mechanical and biochemical changes in the superficial zone of articular cartilage in canine experimental osteoarthritis. J Orthop Res 1994; 12: 474-484.
111. Holmes MH, Lai WM and Mow VC. Singular perturbation analysis of the nonlinear, flow-dependent compressive stress relaxation behavior of articular cartilage. J Biomech Eng 1985; 107: 206-218.
112. Mow VC, Ateshian GA, Lai WM, et al. Effects of fixed charges on the stress relaxation behavior of hydrated soft tissue in a confined compression problem. Int J Solids Struct 1998; 35: 4945-4962.
113. Wang CC, Hung CT and Mow VC. An analysis of the effects of depth-dependent aggregate modulus on articular cartilage stress-relaxation behavior in compression. J Biomech 2001; 34: 75-84.
114. Armstrong CG, Lai WM and Mow VC. An analysis of the unconfined compression of articular cartilage. J Biomech Eng 1984; 106: 165-173.
115. Jurvelin JS, Buschmann MD and Hunziker EB. Optical and mechanical determination of Poisson's ratio of adult bovine humeral articular cartilage. J Biomech 1997; 30: 235-241.
116. Huang C-H, Mow VC and Ateshian GA. The role of flow-independent viscoelasticity in the biphasic tensile and compressive responses of articular cartilage. J Biomech Eng 2001; 123: 410-417.
117. Di Silvestro MR, Zhu Q, Wong M, et al. Biphasic poroviscoelastic simulation of the unconfined compression of articular cartilage. I. Simultaneous prediction of reaction force and lateral displacement. J Biomech Eng 2001; 123: 191-197.
118. Di Silvestro MR, Zhu Q and Suh JK. Biphasic poroviscoelastic simulation of the unconfined compression of articular cartilage. II. Effect of variable strain rates. J Biomech Eng 2001; 123: 198-200.
119. Mow VC, Gibbs MC, Lai WM, et al. Biphasic indentation of articular cartilage. II. A numerical algorithm and an experimental study. J Biomech 1989; 22: 853-861.
120. Athanasiou KA, Rosenwasser MP, Buckwalter JA, et al. Interspecies comparisons of in situ intrinsic mechanical properties of distal femoral cartilage. J Orthop Res 1991; 9: 330-340.
121. Lyyra-Laitinen T, Niinimaki M, Toyras J, et al. Optimization of the arthroscopic indentation instrument for the measurement of thin cartilage stiffness. Phys Med Biol 1999; 44: 2511-2524.
122. Lyyra T, Kiviranta I, Vaatainen U, et al. In vivo characterization of indentation stiffness of articular cartilage in the normal human knee. J Biomed Mater Res 1999; 48: 482-487.
123. Froimson MI, Ratcliffe A, Gardner TR, et al. Differences in patellofemoral joint cartilage material properties and their significance to the etiology of cartilage surface fibrillation. Osteoarthr Cartil 1997; 5: 377-386.
124. Athanasiou KA, Agarwal A and Dzida FJ. Comparative study of the intrinsic mechanical properties of the human acetabular and femoral head cartilage. J Orthop Res 1994; 12: 340-349.
125. Donzelli PS, Spilker RL, Ateshian GA, et al. Contact analysis of biphasic transversely isotropic cartilage layers and correlations with tissue failure. J Biomech 1999; 32: 1037-1047.
126. Ahmed AM, Burke DL and Yu A. In vitro measurement of static pressure distribution in synovial joints. II. Retropatellar surface. J Biomech Eng 1983; 105: 226-236.
127. Ateshian GA, Kwak SD, Soslowsky LJ, et al. A stereophotogrammetric method for determining in situ contact areas in diarthrodial joints, and a comparison with other methods. J Biomech 1994; 27: 111-124.
128. Ateshian GA, Lai WM, Zhu WB, et al. An asymptotic solution for the contact of two biphasic cartilage layers. J Biomech 1994; 27: 1347-1360.
129. Mow VC, Bachrach NM, Setton LA, et al. Stress, strain, pressure, and flow fields in articular cartilage and chondrocytes. In: Mow VC, Guilak F, Tran-Son-Tay R, et al. (eds) Cell mechanics and cellular engineering. New York: Springer-Verlag, 1994, pp.147-171.
130. Sommarin Y, Larsson T and Heinegard D. Chondrocyte-matrix interactions: attachment to proteins isolated from cartilage. Exp Cell Res 1989; 184: 181-192.
131. Han SK, Federico S, Grillo A, et al. The mechanical behavior of chondrocytes predicted with a microstructural model of articular cartilage. Biomech Model Mechanobiol 2007; 6: 139-150.
132. Federico S, Grillo A, La Rosa G, et al. A transversely isotropic, transversely homogeneous microstructuralstatistical model of articular cartilage. J Biomech 2005; 38(10): 2008-2018.
133. Federico S, Herzog W, Wu JZ, et al. A method to estimate the elastic properties of the extracellular matrix of articular cartilage. J Biomech 2004; 37: 401-404.
134. Federico S, Grillo A and Herzog W. A transversely isotropic composite with a statistical distribution of spheroidal inclusions: a geometrical approach to overall properties. J Mech Phys Solids 2004; 52(10): 2309-2327.
135. Wu JZ, Herzog W and Epstein M. Modelling of location-and time-dependent deformation of chondrocytes during cartilage loading. J Biomech 1999; 32: 563-572.
136. Wu JZ and Herzog W. Finite element simulation of location- and time-dependent mechanical behaviour of chondrocytes in unconfined compression tests. Ann Biomed Eng 2000; 28: 318-330.
137. Li LP, Buschmann MD and Shirazi-Adl A. A fibril reinforced nonhomogeneous poroelastic model for articular cartilage: inhomogenous response in unconfined compression. J Biomech 2000; 33: 1533-1541.
138. Schinagl RM, Ting MK, Price JH, et al. Video microscopy to quantify the inhomogeneous equilibrium strain within articular cartilage during confined compression. Ann Biomed Eng 1996; 24: 500-512.
139. Elmore SM, Sokoloff L, Norris G, et al. Nature of "imperfect" elasticity of articular cartilage. J Appl Physiol 1962; 18: 393-396.
140. Mow VC, Ratcliffe A and Poole AR. Cartilage and diarthrodial joints as paradigms for hierarchical materials and structures. Biomaterials 1992; 13: 67-97.
141. Gu WY, Mao XG, Rawlins BA, et al. Streaming potential of human lumbar annulus fibrosus is anisotropic and affected by disc degeneration. J Biomech 1999; 32: 1177-1182.
142. Zienkiewicz OC and Taylor RL. The finite element method. Volume 2. 4th ed. London, McGraw-Hill, 1991.
143. Kempson GE. Mechanical properties of articular cartilage. In: Freeman MAR (ed.) Adult articular cartilage, 2nd ed. Kent: Pitman Medical, 1979, pp.334-414.
144. Kempson GE, Muir H, Pollard C, et al. The tensile properties of the cartilage of human femoral condyles related to the content of collagen and glycosaminoglycans. Biochim Biophys Acta 1973; 297: 456-472.
145. Schmidt MB, Mow VC, Chun LE, et al. Effects of proteoglycan extraction on the tensile behavior of articular cartilage. J Orthop Res 1990; 8: 353-363.
146. Kempson GE. Relationship between the tensile properties of articular cartilage from the human knee and age. Ann Rheum Dis 1982; 41: 508-511.
147. Kempson GE. Age-related changes in the tensile properties of human articular cartilage: a comparative study between the femoral head of the hip joint and the talus of the ankle joint. Biochim Biophys Acta 1991; 1075: 223-230.
148. Soulhat J, Buschmann MD and Shirazi-Adl A. A fibrilnetwork-reinforced biphasic model of cartilage in unconfined compression. J Biomech Eng 1999; 121: 340-347.
149. Bachrach NM, Valhmu WB, Stazzone E, et al. Changes in proteoglycan synthesis of chondrocytes are associated with the time-dependent changes in their mechanical environment. J Biomech 1995; 28: 1561-1569.
150. Guilak F and Mow VC. Determination of the mechanical response of the chondrocyte in situ using confocal microscopy and finite element analysis. In: American Society of Mechanical Engineers advanced in bioengineering, BED, 1992, vol. 22, pp.21-23, Anaheim, CA, USA.
151. Lim CT, Zhou EH and Quek ST. Mechanical model for living cell - a review. J Biomech 2006; 39: 195-216.
152. Mark A, Coughlin F and Stamenovic D. A prestressed cable network model of the adherent cell cytoskeleton. Biophys J 2003; 84: 1328-1336.
153. Sultan C, Stamenovic D and Ingber DE. A computational tensegrity model predicts dynamic rheological behaviors in living cells. Ann Biomed Eng 2004; 32(4): 520-530.
154. Stamenovic D and Ingber DE. Models of cytoskeleton mechanics of adherent cells. Biomech Model Mechanobiol 2002; 1: 95-108.
155. Ingber DE. Tensegrity. II. How structural networks influence cellular information processing networks. J Cell Sci 2003; 116(8): 1397-1408.
156. Ingber D. Opposing views on tensegrity as a structural framework for understanding cell mechanics. J Appl Physiol 2000; 89: 1663-1678.
157. Stamenovic D, Liang Z, Chen J, et al. Effect of the cytoskeletal prestress on the mechanical impedance of cultured airway smooth muscle cells. J Appl Physiol 2002; 92: 1443-1450.
158. Staminovic D, Mijailovich S, Norrelykke I, et al. Cell prestress. II. Contribution of microtubules. Am J Physiol Cell Physiol 2002; 282: 617-624.
159. Ingber D. Tensegrity: the architectural basis of cellular mechanotransduction. Annu Rev Physiol 1997; 59: 575-599.
160. Staminovic D and Wang N. Cellular responses to mechanical stress engineering approaches to cytoskeletal mechanics. J Appl Physiol 2000; 89: 2085-2090.
161. Wang N, Norrelykke IM, Srboljub J, et al. Cell prestress. I. Stiffness and prestress are closely associated in adherent contractile cells. J Cell Physiol 2002; 282: 606-616.
162. Shafrir Y and Forgacs G. Mechanotransduction through the cytoskeleton. Am J Physiol Cell Physiol 2002; 282: 479-486.
163. Evans E and Yeung A. Apparent viscosity and cortical tension of blood granulocytes determined by micropipette aspiration. Biophys J 1989; 56: 151-160.
164. Baesua E, Ruddb RE, Belakb J, et al. Continuum modeling of cell membranes. Int J Non Linear Mech 2004; 39: 369-377.
165. Mills JP, Qie L, Dao M, et al. Nonlinear elastic and viscoelastic deformation of the human red blood cell with optical tweezers.Mech Chem Biosyst 2004; 1(3): 169-180.
166. Kamm RD, McVittie AK and Bathe M. On the role of continuum models in mechanobiology. In: ASME international congress-mechanics in biology, 2000, pp.242-248.
167. Karcher H, Lammerding J, Huang H, et al. A threedimensional viscoelastic model for cell deformation with experimental verification. Biophys J 2003; 85: 3336-3349.
168. McGarry GJ and Prendergast PJ. A three-dimensional finite element model of an adherent eukaryotic cell. Eur Cell Mater 2004; 7: 27-34.
169. Fabry B, Maksym G, Butler J, et al. Scaling the microrheology of living cells. Phys Rev Lett 2001; 87(14): 1-4.
170. Fabry B, Maksym G, Butler J, et al. Time scale and other invariants of integrative mechanical behavior in living cells. Phys Rev E Stat Nonlin Soft Matter Phys 2003; 68: 1-18.
171. Maksym G, Fabry B, Butler J, et al. Mechanical properties of cultured human airway smooth muscle cells from 0.05 to 0.4 Hz. J Appl Physiol 2000; 89: 1619-1632.
172. Sato M, Theret DP, Wheeler LT, et al. Application of the micropipette technique to the measurement of cultured porcine aortic endothelial cell viscoelastic properties. J Biomech Eng 1990; 112(3): 263-268.
173. Mijaailovich S, Kojic M, Zikovic M, et al. A finite element model of cell deformation during magnetic bead twisting. J Appl Physiol 2002; 93: 1429-1436.
174. Adasnwz P, Laurentz V, Oddouw C, et al. A cellular tensegrity model to analyze the structural viscoelasticity of the cytoskeleton. J Theor Biol 2002; 218: 155-173.
175. Sun H, Di S, Zhang N, et al. Micromechanics of composite materials using multivariable finite element method and homogenization theory. Int J Solids Struct 2001; 38: 3007-3020.
176. Park KC, Felippa CA and Rebel G. A simple algorithm for localized construction of non-matching structural interfaces. Int J Numer Methods Eng 2002; 53: 2117-2142.
177. Abusara Z, Seerattan R, Leumann A, et al. A novel method for determining articular cartilage chondrocyte mechanics in vivo. J Biomech 2011; 44: 930-934.