REFERENCES
- AbdullahOM, OthmanSF, ZhouXJ, MaginRL. 2007. Diffusion tensor imaging as an early marker for osteoarthritis. Proc Int Soc Magn Reson Med. 15:814.
- AbousleimanY, ChengAHD, JiangC, RoegiersJC. 1996. Poroviscoelastic analysis of borehole and cylinder problems. Acta Mech. 109(1–4):199–219.
- AndersonAE, EllisBJ, MaasSA, PetersCL, WeissJA. 2008. Validation of finite element predictions of cartilage contact pressure in the human hip joint. J Biomech Eng. 130:051008.
- AndersonAE, EllisBJ, MaasSA, WeissJA. 2010. Effects of idealized joint geometry on finite element predictions of cartilage contact stresses in the hip. J Biomech. 43:1351–1357.
- AteshianGA, ChahineNO, BasaloIM, HungCT. 2004. The correspondence between equilibrium biphasic and triphasic material properties in mixture models of articular cartilage. J Biomech. 37:391–400.
- AteshianGA, EllisBJ, WeissJA. 2007. Equivalence between short-time biphasic and incompressible elastic material responses. J Biomech Eng. 129:405–412.
- AteshianGA, RajanV, ChahineNO, CanalCE, HungCT. 2009. Modeling the matrix of articular cartilage using a continuous fiber angular distribution predicts many observed phenomena. J Biomech Eng. 131:61003.
- AteshianGA, WardenWH, KimJJ, GrelsamerRP, MowVC. 1997. Finite deformation biphasic material properties of bovine articular cartilage from confined compression experiments. J Biomech. 30:1157–1164.
- AteshianGA, WeissJA. 2010. Anisotropic hydraulic permeability under finite deformation. J Biomech Eng. 132:111004.
- AthanasiouKA, DarlingEM, HuJC2010. Articular cartilage tissue engineering. San Rafael: Morgan & Claypool.
- AthanasiouKA, RosenwasserMP, BuckwalterJA, MalininTI, MowVC. 1991. Interspecies comparisons of in situ intrinsic mechanical properties of distal femoral cartilage. J Orthop Res. 9:330–340.
- BachrachNM, MowVC, GuilakF. 1998. Incompressibility of the solid matrix of articular cartilage under high hydrostatic pressures. J Biomech. 31:445–451.
- BettenJ. 1987. Formulation of anisotropic constitutive equations. In: BoehlerJP, editor. Applications of tensor functions in solid mechanics. CISM courses and lectures no. 292. Wien: Springer-Verlag. p. 227–250.
- BishopAW. 1959. The principle of effective stress. Tek Ukebl. 39:859–863.
- BluhmJ. 2002. Modelling of saturated thermo-elastic porous solids with different phase temperatures. In: EhlersW, BluhmJ, editors. Porous media: theory, experiments and numerical applications. Berlin, Heidelberg, New York: Springer-Verlag. p. 87–118.
- BoehlerJP. 1987. Introduction to the invariant formulation of anisotropic constitutive equations. In: BoehlerJP, editor. Applications of tensor functions in solid mechanics. CISM courses and lectures no. 292. Wien: Springer-Verlag. p. 13–30.
- BowenRM. 1980. Incompressible pourous media models by use of theory of mixture. Int J Eng Sci. 18:1129–1148.
- BowenRM. 1982. Compressible porous media models by use of the theory of mixtures. Int J Eng Sci. 20:697–735.
- BuckleyMR, GleghornJP, CohenI, BonassarLJ. 2007. Depth dependence of shear properties in articular cartilage. In: Transactions of the 53rd annual meeting of the orthopaedic research society. San Diego, CA.
- ChahineNO, ChenFH, HungCT, AteshianGA. 2005. Direct measurement of osmotic pressure of glycosaminoglycan solutions by membrane osmometry at room temperature. Biophys J. 89:1543–1550.
- ChahineNO, WangCC, HungCT, AteshianGA. 2004. Anisotropic strain-dependent material properties of bovine articular cartilage in the transitional range from tension to compression. J Biomech. 37:1251–1261.
- ChapelleD, GerbeauJF, Sainte-MarieJ, Vignon-ClementelIE. 2010. A poroelastic model valid in large strains with applications to perfusion in cardiac modeling. J Vasc Interv Radiol. 14:1427–1432.
- ChenAC, BaeWC, SchinaglRM, SahRL. 2001. Depth- and strain-dependent mechanical and electromechanical properties of full-thickness bovine articular cartilage in confined compression. J Biomech. 34:1–12.
- ChenY, ChenX, HisadaT. 2006. Non-linear finite element analysis of mechanical electrochemical phenomena in hydrated soft tissues based on triphasic theory. Int J Numer Methods Eng. 65:147–173.
- ChenAHD, DetournayE. 1998. On singular integral equations and fundamental solutions of poroelasticity. Int J Solids Struct. 35(34/35):4521–4555.
- CoussyO. 2004. Poromechanics. Chichester: John Wiley & Sons.
- de BoerR. 2000. Theory of porous media. Highlights in the historical development and current state. Heidelberg: Springer-Verlag.
- DelfinoA, StergiopulosN, MooreJE, Jr, MeisterJJ. 1997. Residual strain effects on the stress field in a thick wall finite element model of the human carotid bifurcation. J Biomech. 30:777–786.
- DemirayH. 1972. A note on the elasticity of soft biological tissues. J Biomech. 5:309–311.
- deVisserSK, BowdenJC, Wentrup-BryneE, RintoulL, BostromT, PopeJM, MomotKI. 2008a. Anisotropy of collagen fibre alignment in bovine cartilage: comparison of polarised light microscopy and spatially resolved diffusion-tensor measurements. Osteoarthritis Cartilage. 16:689–697.
- deVisserSK, CrawfordRW, PopeJM. 2008b. Structural adaptations in compressed articular cartilage measured by diffusion tensor imaging. Osteoarthritis Cartilage. 16:83–89.
- EhlersW. 1989. Poröse Medien – ein kontinuumsmechanisches Modell auf der Basis der MischungstheorieUniversität GH Essen. Forschungsbericht aus dem Fachbereich Bauwesen. 47.
- EhlersW. 1993. Constitutive equations for granular materials in geomechanical context. In: HutterK, editor. Continuum mechanics in environmental sciences and geophysics. CISM courses and lectures no. 337. Wien: Springer-Verlag. p. 313–402.
- EhlersW. 2002. Foundations of multiphasic and porous materials. In: EhlersW, BluhmJ, editors. Porous media: theory, experiments and numerical applications. Berlin: Springer-Verlag. p. 3–86.
- EhlersW, EipperG. 1997. Finite elastizität bei uidgesättigten hochporösen festkörpern. Z Angew Math Mech. 77:79–80.
- EhlersW, EipperG. 1999. Finite elastic deformations in liquid-saturated and empty porous solids. Transport Porous Med. 34:179–191.
- EhlersW, KarajanN, MarkertB. 2009. An extended biphasic model for charged hydrated tissues with application to the intervertebral disc. Biomech Model Mechanobiol. 8:233–251.
- Eipper G. 1998. Theorie und Numerik finiter elastischer Deformationen in fluidgesättigten porösen FestkörpernUniversität Stuttgart. Bericht Nr. II-1 aus dem Institut für Mechanik (Bauwesen).
- ElliottDM, NarmonevaDA, SettonLA. 2002. Direct measurement of the Poisson's ratio of human patella cartilage in tension. J Biomech Eng. 124:223–228.
- ErneOK, ReidJB, EhmkeLW, SommersMB, MadeySM, BottlangM. 2005. Depth-dependent strain of patellofemoral articular cartilage in unconfined compression. J Biomech. 38:667–672.
- FedericoS, GasserTC. 2010. Nonlinear elasticity of biological tissues with statistical fibre orientation. J R Soc Interface. 7:955–966.
- FedericoS, GrilloA. 2012. Elasticity and permeability of porous fibre reinforced materials under large deformations. Mech Mater. 44:58–71.
- FedericoS, HerzogW. 2008. On the anisotropy and inhomogeneity of permeability in articular cartilage. Biomech Model Mechanobiol. 7:367–378.
- FilidoroL, DietrichO, WeberJ, RauchE, OetherT, WickM, ReiserMF, GlaserC. 2005. High-resolution diffusion tensor imaging of human patellar cartilage: feasibility and preliminary findings. Magn Reson Med. 53:993–998.
- GarcíaJJ, CortésDH. 2007. A biphasic viscohyperelastic fibril-reinforced model for articular cartilage: formulation and comparison with experimental data. J Biomech. 40:1737–1744.
- GasserTC, OgdenRW, HolzapfelGA. 2006. Hyperelastic modelling of arterial layers with distributed collagen fibre orientations. J R Soc Interface. 3:15–35.
- Goreham-VossCM, McKinleyTO, BrownTD. 2007. A finite element exploration of cartilage stress near an articular incongruity during unstable motion. J Biomech. 40:3438–3447.
- GuKB, LiLP. 2011. A human knee joint model considering fluid pressure and fiber orientation in cartilages and menisci. Med Eng Phys. 33:497–503.
- HanSK, FedericoS, EpsteinM, HerzogW. 2005. An articular cartilage contact model based on real surface geometry. J Biomech. 38:179–184.
- HassanizadehSM, GrayWG. 1979a. General conservation equations for multi-phase systems: 1. Averaging procedure. Adv Water Resour. 2:131–144.
- HassanizadehSM, GrayWG. 1979b. General conservation equations for multi-phase systems: 2. Mass, momenta, energy, and entropy equations. Adv Water Resour. 2:191–208.
- HassanizadehSM, GrayWG. 1980. General conservation equations for multi-phase systems: 3. Constitutive theory for porous media flow. Adv Water Resour. 3:25–40.
- HassanizadehSM, GrayWG. 1990. Mechanics and thermodynamics of multiphase flow in porous media including interphase boundaries. Adv Water Resour. 13:169–186.
- HolmesMH, LaiWM, MowVC. 1985. Singular perturbation analysis of the nonlinear, flow-dependent compressive stress relaxation behavior of articular cartilage. J Biomed Eng. 107:206–218.
- HolzapfelGA, SommerG, GasserCT, RegitnigP. 2005a. Determination of the layer-specific mechanical properties of human coronary arteries with non-atherosclerotic intimal thickening, and related constitutive modelling. Am J Physiol Heart Circ Physiol. 289:H2048–H2058.
- HolzapfelGA, StadlerM, GasserTC. 2005b. Changes in the mechanical environment of stenotic arteries during interaction with stents: computational assessment of parametric stent design. J Biomech Eng. 127:166–180.
- HuangCY, MowVC, AteshianGA. 2001. The role of flow-independent viscoelasticity in the biphasic tensile and compressive responses of articular cartilage. J Biomech Eng. 123:410–417.
- HuangCY, SoltzMA, KopaczM, MowVC, AteshianGA. 2003. Experimental verification of the roles of intrinsic matrix viscoelasticity and tension–compression nonlinearity in the biphasic response of cartilage. J Biomech Eng. 125:84–93.
- HuangCY, StankiewiczA, AteshianGA, MowVC. 2005. Anisotropy, inhomogeneity, and tension-compression nonlinearity of human glenohumeral cartilage in finite deformation. J Biomech. 38:799–809.
- HumphreyJD. 2002. Cardiovascular solid mechanics. Cells, tissues, and organs. New York: Springer-Verlag.
- JoshiMD, SuhJK, MaruiT, WooSLY. 1995. Interspecies variation of compressive biomechanical properties of the meniscus. J Biomed Mater Res. 29:823–828.
- JulkunenP, KivirantaP, WilsonW, JurvelinJS, KorhonenRK. 2007. Characterization of articular cartilage by combining microscopic analysis with a fibril-reinforced finite-element model. J Biomech. 40:1862–1870.
- JulkunenP, WilsonW, JurvelinJS, RieppoJ, QuCJ, LammiMJ, KorhonenRK. 2008. Stress-relaxation of human patellar articular cartilage in unconfined compression: prediction of mechanical response by tissue composition and structure. J Biomech. 41:1978–1986.
- JurvelinJS, BuschmannMD, HunzikerEB. 1997. Optical and mechanical determination of Poisson's ratio of adult bovine humeral articular cartilage. J Biomech. 30:235–241.
- KorhonenRK, LaasanenMS, TöyräsJ, LappalainenR, HelminenHJ, JurvelinJS. 2003. Fibril reinforced poroelastic model predicts specifically mechanical behavior of normal, proteoglycan depleted and collagen degraded articular cartilage. J Biomech. 36:1373–1379.
- LaiWM, HouJS, MowVC. 1991. A triphasic theory for the swelling and deformation behaviours of articular cartilage. J Biomech Eng. 113:245–258.
- LiLP, BuschmannMD, Shirazi-AdlA. 2000. A fibril reinforced nonhomogeneous poroelastic model for articular cartilage: inhomogeneous response in unconfined compression. J Biomech. 33:1533–1541.
- LiLP, CheungJTM, HerzogW. 2009. Three-dimensional fibril-reinforced finite element model of articular cartilage. Med Biol Eng Comput. 47:607–615.
- LiLP, HerzogW. 2004. The role of viscoelasticity of collagen fibers in articular cartilage: theory and numerical formulation. Biorheology. 41:181–194.
- LiG, LopezO, RubashH. 2001. Variability of a three-dimensional finite element model constructed using magnetic resonance images of a knee for joint contact stress analysis. J Biomech Eng. 123:341–346.
- LilledahlMB, PierceDM, RickenT, HolzapfelGA, de Lange DaviesC. 2011. Structural analysis of articular cartilage using multiphoton microscopy: input for biomechanical modeling. IEEE Trans Med Imaging. 30(9):1635–1648.
- MandaK, RydL, ErikssonA. 2011. Finite element simulations of a focal knee resurfacing implant applied to localized cartilage defects in a sheep model. J Biomech. 44:794–801.
- MansourJM. 2008. Biomechanics of cartilage. In: OatisCA, editor. Kinesiology: The Mechanics and Pathomechanics of Human Movement, 2nd Ed., Philadelphia: Lippincott Williams and Wilkins. p. 69–83.
- MarkertB. 2007. A constitutive approach to 3-D nonlinear fluid flow through finite deformable porous continua. Transport Porous Med. 70:427–450.
- MederR, deVisserSK, BowdenJC, BostromT, PopeJM. 2006. Diffusion tensor imaging of articular cartilage as a measure of tissue microstructure. Osteoarthritis Cartilage. 14:875–881.
- MononenM, MikkolaM, JulkunenP, OjalaR, NieminenM, JurvelinJ, KorhonenR. 2012. Effect of superficial collagen patterns and fibrillation of femoral articular cartilage on knee joint mechanics – a 3D finite element analysis. J Biomech. 45(3):579–587.
- MowVC, GibbsMC, LaiWM, ZhuWB, AthanasiouKA. 1989. Biphasic indentation of articular cartilage-II. A numerical algorithm and an experimental study. J Biomech. 22:853–861.
- MowVC, GuWY, ChenFH. 2005. Structure and function of articular cartilage and meniscus. In: MowVC, HuiskesR, editors. Basic orthopaedic biomechanics & mechano-biology. 3rd ed. Philadelphia: Lippincott Williams & Wilkins. p. 181–258.
- ParkS, KrishnanR, NicollSB, AteshianGA. 2003. Cartilage interstitial fluid load support in unconfined compression. J Biomech. 36:1785–1796.
- PeñaE, CalvoB, MartínezMA, PalancaD, DoblaréM. 2005. Finite element analysis of the effect of meniscal tears and meniscectomies on human knee biomechanics. Clin Biomech. p. 498–507.
- PierceDM, TrobinW, RayaJG, TrattnigS, BischofH, GlaserC, HolzapfelGA. 2010. DT-MRI based computation of collagen fiber deformation in human articular cartilage: a feasibility study. Ann Biomed Eng. 38:2447–2463.
- PierceDM, TrobinW, TrattnigS, BischofH, HolzapfelGA. 2009. A phenomenological approach toward patient-specific computational modeling of articular cartilage including collagen fiber tracking. J Biomech Eng. 131:091006.
- PotterHG, BlackBR, ChongLR. 2009. New techniques in articular cartilage imaging. Clin Sports Med. 28:77–94.
- ResponteDJ, NatoliRM, AthanasiouKA. 2007. Collagens of articular cartilage: structure, function, and importance in tissue engineering. Crit Rev Biomed Eng. 35:363–411.
- ReynaudB, QuinnTM. 2006. Anisotropic hydraulic permeability in compressed articular cartilage. J Biomech. 39:131–137.
- RickenT, BluhmJ. 2009. Evolutional growth and remodeling in multiphase living tissue. Comp Mater Sci. 45:806–811.
- RickenT, BluhmJ. 2010. Remodeling and growth of living tissue: a multiphase theory. Arch Appl Mech. 80:453–465.
- RickenT, DahmenU, DirschO. 2010. A biphasic model for sinusoidal liver perfusion remodeling after outflow obstruction. Biomech Model Mechanobiol. 9:435–450.
- SimoJC, PisterKS. 1984. Remarks on rate constitutive equations for finite deformation problems: computational implications. Comput Methods Appl Mech Engrg. 46:201–215.
- SkemptonAW. 1960. Terzaghi's discovery of effective stress. In: BjerrumL, CasagrandeA, PeckRB, SkemptonAW, editors. From theory to practice in soil mechanics. New York, London: John Wiley. p. 42–53.
- SoltzMA, AteshianGA. 1998. Experimental verification and theoretical prediction of cartilage interstitial fluid pressurization at an impermeable contact interface in confined compression. J Biomech. 31:927–934.
- SoltzMA, AteshianGA. 2000. A conewise linear elasticity mixture model for the analysis of tension-compression nonlineartiy in articular cartilage. J Biomech Eng. 122:576–586.
- SpencerAJM. 1971. Part III. Theory of invariants. In: EringenAC, editor. Continuum physics. New York: Academic Press. p. 239–353.
- SunW, ChaikofEL, LevenstonME. 2008. Numerical approximation of tangent moduli for finite element implementations of nonlinear hyperelastic material models. J Biomech Eng. 130:061003.
- TongJ, CohnertT, RegitnigP, HolzapfelGA. 2011. Effects of age on the elastic properties of the intraluminal thrombus and the thrombus-covered wall in abdominal aortic aneurysms: biaxial extension behavior and material modeling. Eur J Vasc Endovasc Surg. 42:207–219.
- van LoonR, HuygheJ, WijlaarsM, BaaijensF. 2003. 3D FE implementation of an incompressible quadriphasic mixture model. Int J Numer Methods Eng. 57:1243–1258.
- WangL, FrittonSP, WeinbaumS, CowinSC. 2003. On bone adaptation due to venous stasis. J Biomech. 36:1439–1451.
- WhitakerS. 1977. Simultaneous heat, mass, and momentum transfer in porous media: a theory of drying. Adv Heat Transfer. 13:119–203.
- WilsonW, HuygheJM, van DonkelaarCC. 2007. Depth-dependent compressive equilibrium properties of articular cartilage explained by its composition. Biomech Model Mechanobiol. p. 43–53.
- WilsonW, van DonkelaarCC, van RietbergenB, HuiskesR. 2005. A fibril-reinforced poroviscoelastic swelling model for articular cartilage. J Biomech. 38:1195–1204.
- WilsonW, van DonkelaarCC, van RietbergenB, ItoK, HuiskesR. 2004. Stresses in the local collagen network of articular cartilage: a poroviscoelastic fibril-reinforced finite element study. J Biomech. 37:357–366.
- WongBL, BaeWC, ChunJ, GratzKR, SahRL. 2007. Micro-mechanics of cartilage articulation: effect of degeneration on shear deformation. In: Transactions of the 53rd annual meeting of the orthopaedic research society. San Diego, CA.
- WongM, PonticielloM, KovanenV, JurvelinJS. 2000. Volumetric changes of articular cartilage during stress relaxation in unconfined compression. J Biomech. 33:1049–1054.
- ZhengQS, SpencerAJM. 1993a. On the canonical representations for Kronecker powers of orthogonal tensors with application to material symmetry problems. Int J Eng Sci. 4:617–635.
- ZhengQS, SpencerAJM. 1993b. Tensors which characterize anisotropies. Int J Eng Sci. 5:679–693.
- ZipfelWR, WilliamsRM, WebbWW. 2003. Nonlinear magic: multiphoton microscopy in the biosciences. Nat Biotechnol. 21:1368–1376.