On the anisotropy and inhomogeneity of permeability in articular cartilage
Tóm tắt
Articular cartilage is known to be anisotropic and inhomogeneous because of its microstructure. In particular, its elastic properties are influenced by the arrangement of the collagen fibres, which are orthogonal to the bone-cartilage interface in the deep zone, randomly oriented in the middle zone, and parallel to the surface in the superficial zone. In past studies, cartilage permeability has been related directly to the orientation of the glycosaminoglycan chains attached to the proteoglycans which constitute the tissue matrix. These studies predicted permeability to be isotropic in the undeformed configuration, and anisotropic under compression. They neglected tissue anisotropy caused by the collagen network. However, magnetic resonance studies suggest that fluid flow is “directed” by collagen fibres in biological tissues. Therefore, the aim of this study was to express the permeability of cartilage accounting for the microstructural anisotropy and inhomogeneity caused by the collagen fibres. Permeability is predicted to be anisotropic and inhomogeneous, independent of the state of strain, which is consistent with the morphology of the tissue. Looking at the local anisotropy of permeability, we may infer that the arrangement of the collagen fibre network plays an important role in directing fluid flow to optimise tissue functioning.
Tài liệu tham khảo
Arokoski JPA, Hyttinen MM, Lapveteläinen T, Takács P, Kosztáczky B, Módis L, Kovanen V, Helminen HJ (1996) Decreased birefringence of the superficial zone collagen network in the canine knee (stifle) articular cartilage after long distance running training, detected by quantitative polarised light microscopy. Ann Rheumat Dis 55:253–264
Aspden R, Hukins D (1981) Collagen organization in articular cartilage, determined by X-ray diffraction, and its relationship to tissue function. Proc Roy Soc Lond Ser B 212:299–304
Bencsik M, Ramanathan C (2001) Direct measurement of porous media local hydrodynamical permeability using gas MRI. Magn Reson Imaging 19:379–383
Benninghoff A (1925) Form und Bau der Glenkknorpel in ihren Beziehungen zur Funktion. II: Der Aufbau des Glenkknorpel in seinen Beziehungen zur Funktion, Zeitschrift für Zellforschung 2:783–862
Chen AC, Bae WC, Schinagl RM, Sah RL (2001) Depth- and strain-dependent mechanical and electrochemical properties of full-thickness bovine articular cartilage in confined compression. J Biomech 34:1–12
Clark AL, Barclay LD, Matyas JR, Herzog W (2003) In situ chondrocyte deformation with physiological compression of the feline patellofemoral joint. J Biomech 36:553–568
Clark AL, Leonard TR, Barclay LD, Mathyas JR, Herzog W (2006) Heterogeneity in patellofemoral cartilage adaptation to anterior cruciate ligament transection; chondrocyte shape and deformation with compression. Osteoarthr Cartil 14:120–130
Curtin WA, Reville WJ (1995) Ultrastructural observations on fibril profiles in normal and degenerative human articular cartilage. Clin Orthop Relat Res 313:224–230
Farquhar T, Dawson PR, Torzilli PA (1990) A microstructural model for the anisotropic drained stiffness of articular cartilage. J Biomech Eng 112:414–424
Federico S, Grillo A, Herzog W (2004) A transversely isotropic composite with a statistical distribution of spheroidal inclusions: a geometrical approach to overall properties. J Mech Phys Solids 52(10):2309–2327
Federico S, Grillo A, La Rosa G, Giaquinta G, Herzog W (2005) A transversely isotropic, transversely homogeneous microstructural- statistical model of articular cartilage. J Biomech 38(10):2008–2018
Federico S, Herzog W (2007) On the permeability of fibre-reinforced porous materials. (submitted)
Fullerton GD, Rahal A (2007) Collagen structure: the molecular source of tendon magic angle effect. J Magn Reson Imaging 25(2):345–361
Han S, Gemmell SJ, Helmer KG, Grigg P, Wellen JW, Hoffman AH, Sotak CH (2000) Changes in ADC caused by tensile loading of rabbit achilles tendon: evidence for water transport. J Magn Reson 144(2):217–227
Hedlund H, Mengarelli-Widholm S, Reinholt F, Svensson O (1993) Stereological studies on collagen in bovine articular cartilage. Acta Pathol Microbiol Immunol Scand 101:133–140
Herzog W, Federico S (2006) Considerations on joint and articular cartilage mechanics. Biomech Model Mechanobiol 5(2–3):64–81
Higginson GR, Litchfield MR, Snaith J (1976) Load–displacement–time characteristics of articular cartilage. Int J Mech Sci 18:481–486
Holmes MH, Mow VC (1990) The non-linear characteristics of soft gels and hydrated connective tissues in ultrafiltration. J Biomech 23:1145–1156
Jeffery AK, Blunn GW, Archer CW, Bentley G (1991) Three-dimensional collagen architecture in bovine articular cartilage. J Bone Joint Surg (Br) 73B:795–801
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. Trans Orthop Res Soc 22(1):199
Kiviranta P, Rieppo J, Korhonen RK, Julkunen P, Töyräs J, Jurvelin JS (2006) Collagen network primarily controls poisson’s ratio of bovine articular cartilage in compression. J Orthop Res 24:690–699
Kuwabara S (1959) The forces experienced by randomly distributed parallel circular cylinders or spheres in a viscous flow at small Reynolds numbers. J Phys Soc Jpn 14:527–532
Landau LD, Lifshitz EM (1960) Electrodynamics of continuous media. Pergamon, Oxford
Lå ngsjö TK, Hyttinen M, Pelttari A, Kiraly K, Arokoski J, Helminen HJ (1999) Electron microscopic stereological study of collagen fibrils in bovine articular cartilage: volume and surface densities are best obtained indirectly (from length densities and diameters) using isotropic uniform random sampling. J Anat 195:281–293
Maroudas A (1968) Physicochemical properties of cartilage in the light of ion-exchange theory. Biophys J 8:575–595
Maroudas A, Bullough P (1968) Permeability of articular cartilage. Nature 219:1260–1261
Maroudas A (1975) Biophysical chemistry of cartilaginous tissue with special reference to solute and fluid transport. Biorheology 12:233–248
Maroudas A (1976) Balance between swelling pressure and collagen tension in normal and degenerate cartilage. Nature 260:808–809
Maroudas A, Mizrahi, J, BenHaim E, Ziv I (1987) Swelling pressure in cartilage. Adv Microcirc 13:203–212
McLaughlin R (1977) A study of the differential scheme for composite materials. Int J Eng Sci 15:237–244
Mollenahuer J, Aurich M, Muehleman C, Khelashvilli G (2003) X-Ray diffraction of the molecular substructure of human articular cartilage. Connect Tissue Res 44:201–207
Mow VC, Holmes MH, Lai WM (1984) Fluid transport and mechanical properties of articular cartilage: a review. J Biomech 17:377–394
Mow VC, Kuei SC, Lai WM, Armstrong CG (1980) Biphasic creep and stress relaxation of articular cartilage, theory and experiment. J Biomech Eng 102:73–84
Muir H, Bullough P, Maroudas A (1970) The distribution of collagen in human articular cartilage with some of its physiological implications. J Bone Joint Surg 52B:554–563
Norris AN (1985) A differential scheme for the effective moduli of composites. Mech Mater 4:1–16
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
Podzniakov S, Tsang C-F (2000) A self-consistent approach for calculating the effective hydraulic conductivity of a binary, Heterogeneous Medium. Water Resour Res 40(W05105):1–13
Pollack GH (2001) Cells, gels and the engines of life. Ebner, Seattle, USA
Qiu YP, Weng GJ (1990) On the application of the Mori-Tanaka theory involving transversely isotropic spheroidal inclusions. Int J Eng Sci 28:1121–1137
Quinn TM, Dierickx P, Grodzinsky AJ (2001) Glycosaminoglycan Network Geometry may contribute to anisotropic hydraulic permeability in cartilage under compression. J Biomech 34:1483–1490
Reynaud B, Quinn TM (2006) Anisotropic hydraulic permeability in compressed articular cartilage. J Biomech 39:131–137
Setton LA, Zhu WB, Mow VC (1993) The biphasic poroviscoelastic behavior of articular cartilage: role of the surface zone in governing the compressive behavior. J Biomech 26:581–592
Shin D, Athanasiou KA (1997) Biomechanical properties of the individual cell. Trans Orthop Res Society 22(1):352
Shvidler MI (1985) Stochastic Hydrodynamics of Porous Medium (in Russian). Nedra, Moscow, Russia
Stockwell RA (1979) Biology of cartilage cells. Cambridge University Press, Cambridge
Walpole LJ (1981) Elastic behavior of composite materials: theoretical foundations. Adv Appl Mech 21:169–242
Wang CC-B, Chahine NO, Hung CT, Ateshian GA (2003) Optical determination of anisotropic material properties of bovine articular cartilage in compression. J Biomech 36:339–353
Wellen J, Helmer KG, Grigg P, Sotak CH (2004) Application of porous-media theory to the investigation of water ADC changes in rabbit Achilles tendon caused by tensile loading. J Magn Resonance 170:49–55
Wilson W, van Donkelaar CC, van Rietbergen B, Ito K, Huiskes R (2004) Stresses in the Local Collagen Network of articular cartilage: a poroviscoelastic fibril-reinforced finite element study. J Biomech 37:357–366
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
Wu JZ, Herzog W (2002) Elastic anisotropy of articular cartilage is associated with the micro-structures of collagen fibers and chondrocytes. J Biomech 35:931–942
Xia Y, Moody JB, Alhadlaq H (2002) Orientational dependence of T2 relaxation in articular cartilage: a microscopic MRI (microMRI) study. Magn Reson Med 48(3):460–469