A poroviscohyperelastic model for numerical analysis of mechanical behavior of single chondrocyte

References

• ABAQUS. 1996. ABAQUS/standard user's manual (version 5.6). Pawtucket (RI): Hibbitt, Karlsson & Sorensen, Inc.
   Google Scholar
• Ateshian GA, Costa KD, Hung CT. 2007. A theoretical analysis of water transport through chondrocytes. Biomech Model Mechanobiol. 6:91–101.
   PubMed Web of Science ®Google Scholar
• Baaijens FPT, Trickey WR, Laursen TA, Guilak F. 2005. Large deformation finite element analysis of micropipette aspiration to determine the mechanical properties of the chondrocyte. Ann Biomed Eng. 33(4):494–501.
   PubMed Web of Science ®Google Scholar
• Biot MA. 1941. General theory of three-dimensional consolidation. J Appl Phys. 12:155–164.
   Web of Science ®Google Scholar
• Darling EM, Zauscher S, Block JA, Guilak F. 2007. A thin-layer model for viscoelastic, stress-relaxation testing of cells using atomic force microscopy: do cell properties reflect metastatic potential. Biophys J. 92:1784–1791.
   PubMed Web of Science ®Google Scholar
• Darling EM, Zauscher S, Guilak F. 2006. Viscoelastic properties of zonal articular chondrocytes measured by atomic force microscopy. Osteoarthr Cartilage. 14:571–579.
   PubMed Web of Science ®Google Scholar
• Faria EC, Ma N, Gazi E, Gardner P, Brown M, Clarke NW, Snook RD. 2008. Measurement of elastic properties of prostate cancer cells using AFM. Analyst. 133:1498–1500.
   PubMed Web of Science ®Google Scholar
• Franz CM, Puech PH. 2008. Atomic force microscopy: a versatile tool for studying cell morphology, adhesion and mechanics. Cell Mol Bioeng. 1(4):289–300.
   Web of Science ®Google Scholar
• Higginson GR, Norman R. 1974. The lubrication of porous elastic solids with reference to the functioning of human joints. J Mech Eng Sci. 16(4):250–257.
   Web of Science ®Google Scholar
• Holmes MH, Mow VC. 1990. The nonlinear characteristics of soft gels and hydrated connective tissues in ultrafiltration. J Biomech. 23(11):1145–1156.
   PubMed Web of Science ®Google Scholar
• Jones WR, Ting-Beall HP, Lee GM, Kelley SS, Hochmuth RM, Guilak F. 1997. Mechanical properties of human chondrocytes and chondrons from normal and osteoarthritic cartilage. Paper presented at the 43rd Annual Meeting, Orthopaedic Research Society, San Francisco, CA.
   Google Scholar
• Kaufmann MV. 1996. Porohyperelastic analysis of large arteries including species transport and swelling effects [Ph.D. dissertation]. The University of Arizona: Tucson (AZ).
   Google Scholar
• Kuznetsova TG, Starodubtseva MN, Yegorenkov NI, Chizhik SA, Zhanov RI. 2007. Atomic force microscopy probing of cell elasticity. Micron. 38:824–833.
   PubMed Web of Science ®Google Scholar
• Lin DC, Dimitriadis EK, Horkay F. 2007. Elasticity of rubber-like materials measured by AFM nanoindentation. eXPRESS Polym Lett. 1(9):576–584.
   Web of Science ®Google Scholar
• McCutchen CW. 1982. Cartilage is poroelastic, not viscoelastic (including and exact theorem about strain energy and viscous loss, and an order of magnitude relation for equilibration time). J Biomech. 15(4):325–327.
   PubMed Web of Science ®Google Scholar
• McCutchen CW. 1998. Consolidation theory derived without invoking porosity. Int J Solids Struct. 35(1–2):69–81.
   Web of Science ®Google Scholar
• Meroi EA, Natali AN, Schrefler BA. 1999. A porous media approach to finite deformation behaviour in soft tissues. Comput Methods Biomech Biomed Eng. 2:157–170.
   PubMedGoogle Scholar
• Moo EK, Herzog W, Han SK, Abu Osman NA, Pingguan-Murphy B, Federico S. 2012. Mechanical behaviour of in-situ chondrocytes subjected to different loading rates: a finite element study. Biomech Model Mechanobiol. 11:983–993.
   PubMed Web of Science ®Google Scholar
• Mow VC, Kuei SC, Lai WM, Armstrong CG. 1980. Biphasic creep and stress relaxation of articular cartilage in compression? Theory and experiments. J Biomech Eng. 102(1):73–84.
   PubMed Web of Science ®Google Scholar
• Mow VC, Ratcliffe A, Poole AR. 1992. Cartilage and diarthrodial joints as paradigms for hierarchical materials and structures. Biomaterials. 13(2):67–97.
   PubMed Web of Science ®Google Scholar
• Nguyen TC. 2005. Mathematical modelling of the biomechanical properties of articular cartilage [Ph.D. thesis]. Brisbane: Queensland University of Technology.
   Google Scholar
• Oloyede A, Broom ND. 1991. Is classical consolidation theory applicable to articular cartilage deformation? Clin Biomech. 6(4):206–212.
   PubMed Web of Science ®Google Scholar
• Oloyede A, Broom ND. 1994. The generalized consolidation of articular cartilage: an investigation of its near-physiological response to static load. Connect Tissue Res. 31(1):75–86.
   PubMed Web of Science ®Google Scholar
• Oloyede A, Broom ND. 1996. The biomechanics of cartilage load-carriage. Connect Tissue Res. 34(2):119–143.
   PubMed Web of Science ®Google Scholar
• Oloyede A, Flachsmann R, Broom ND. 1992. The dramatic influence of loading velocity on the compressive response of articular cartilage. Connect Tissue Res. 27:211–224.
   PubMed Web of Science ®Google Scholar
• Rico F, Roca-Cusachs P, Gavara N, Farre R, Rotger M, Navajas D. 2005. Probing mechanical properties of living cells by atomic force microscopy with blunted pyramidal cantilever tips. Phys Rev E. 72(021914):1–10.
   Google Scholar
• Sherwood JD. 1993. Biot poroelasticity of a chemically active shale. Proc R Soc Lond A. 440:365–377.
   Web of Science ®Google Scholar
• Shieh AC, Koay EJ, Athanasiou KA. 2006. Strain-dependent recovery behavior of single chondrocytes. Biomech Model Mechanobiol. 5:172–179.
   PubMed Web of Science ®Google Scholar
• Simon BR. 1992. Multiphase poroelastic finite element models for soft tissue structures. Appl Mech Rev. 45(6):191–219.
   Google Scholar
• Simon BR, Gaballa MA. 1989. Total Lagrangian ‘porohyperelastic’ finite element models of soft tissue undergoing finite strain.pdf. In: Rubinsky B, editor. 1989 In Advances in bioengineering. BED-Vol. 15. New York: ASME; p. 97–98.
   Google Scholar
• Simon BR, Kaufmann MV, McAfee MA, Baldwin AL. 1998. Porohyperelastic finite element analysis of large arteries using ABAQUS. ASME J Biomech Eng. 120:296–298.
   PubMed Web of Science ®Google Scholar
• Simon BR, Kaufmann MV, McAfee MA, Baldwin AL, Wilson LM. 1998. Identification and determination of material properties for porohyperelastic analysis of large arteries. ASME J Biomech Eng. 120:188–194.
   PubMed Web of Science ®Google Scholar
• Simon BR, Liable JP, Pflaster D, Yuan Y, Krag MH. 1996. A poroelastic finite element formulation including transport and swelling in soft tissue structures. J Biomech Eng. 118:1–9.
   PubMed Web of Science ®Google Scholar
• Singh S, Jones BJ, Crawford RW, Xiao Y. 2008. Characterization of a mesenchymal-like stem cell population from osteophyte tissue. Stem Cells Dev. 17(2):245–254.
   PubMed Web of Science ®Google Scholar
• Terzaghi K. 1943. Theoritical soil mechanics. New York: John Wiley.
   Google Scholar
• Touhami A, Nysten B, Dufrene YF. 2003. Nanoscale mapping of the elasticity of microbial cells by atomic force microscopy. Langmuir. 19:4539–4543.
   Web of Science ®Google Scholar
• Trickey WR, Baaijens FPT, Laursen TA, Alexopoulos LG, Guilak F. 2006. Determination of the Poisson's ratio of the cell: recovery properties of chondrocytes after release from complete micropipette aspiration. J Biomech. 39(1):78–87.
   PubMed Web of Science ®Google Scholar
• Trickey WR, Lee GM, Guilak F. 2000. Viscoelastic properties of chondrocytes from normal and osteoarthritic human cartilage. J Orthop Res. 18:891–898.
   PubMed Web of Science ®Google Scholar
• Wu JZ, Herzog W. 2000. Finite element simulation of location- and time-dependent mechanical behavior of chondrocytes in unconfined compression tests. Ann Biomed Eng. 28:318–330.
   PubMed Web of Science ®Google Scholar
• Zhang CY, Zhang YW. 2007. Effects of membrane pre-stress and intrinsic viscoelasticity on nanoindentation of cells using AFM. Philos Mag. 87(23):3415–3435.
   Web of Science ®Google Scholar
• Zhao R, Wyss K, Simmons CA. 2009. Comparison of analytical and inverse finite element approaches to estimate cell viscoelastic properties by micropipette aspiration. J Biomech. 42:2768–2773.
   PubMed Web of Science ®Google Scholar
• Zhou EH, Lim CT, Quek ST. 2005. Finite element simulation of the micropipette aspiration of a living cell undergoing large viscoelastic deformation. Mech Adv Mater Struct. 12(6):501–512.
   Web of Science ®Google Scholar