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Modelling electronic and elastic properties of cartilage

Wybrane pełne teksty z tego czasopisma
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The aim of the paper is to propose a novel approach to modelling the macroscopic electromechanical behaviour of cartilage within the framework of linear response. The cartilage is treated as multiphase material with four constituents: anions, cations, viscous fluid and piezoelectric skeleton. The macroscopic equations were derived by using homogenization methods. Only stationary flow was studied. The elastic macroscopic moduli were determined by assuming, after Broom [60], the honeycomb microstructure of the cartilage. Mathematical developments are preceded by a review of structure and properties of a cartilage.
Rocznik
Strony
283--313
Opis fizyczny
Bibliogr. 67 poz., rys., tab., wykr.
Twórcy
autor
  • Institute of Fundamental Technological Research Polish Academy of Sciences Świętokrzyska 21, Warsaw, Poland
autor
  • Institute of Fundamental Technological Research Polish Academy of Sciences Świętokrzyska 21, Warsaw, Poland
autor
  • Institute of Fundamental Technological Research Polish Academy of Sciences Świętokrzyska 21, Warsaw, Poland
Bibliografia
  • 1. A. BENNINGHOFF, Form und Bau der Gelenkknorpel in ihren Beziehungen zur Funktion [In:] Der Aufbau des Gelenkknorpels in seinen Beziehungen zur Funktion, Zweiter Teil, Z. Zellforsch. mikr. Anat. 2, 783-862, 1925.
  • 2. A. MAROUDAS, Physicochemical properties of articular cartilage [In:] Adult articular cartilage, M.A. R. FREEMAN [Ed.], Pitman Medical, Kent, UK 1979.
  • 3. R. A. STOCKWELL, Biology of cartilage cells, Cambridge University Press, Cambridge 1979.
  • 4. N.D. BROOM and D. B. MYERS, A study of the structural response of wet hyaline cartilage to various loading situations, Connect. Tiss. Res., 7, 227-237, 1980.
  • 5. C. VAN MOW, F. GUILAK, R. TRAN-SON-tay, R. M. HocHMUTH, Cell mechanics and cellular engineering, Springer-Verlag, New York 1994.
  • 6. K. J. GOOCH and C. J. TENNANT, Mechanical forces: their effects on cells and tissues, Springer-Verlag, Berlin, New York 1997.
  • 7. J. F. STOLTZ, X. WANG, S. MULLER and V. LABRADOR, Introduction to the mechanobiology of cells, App. Mech. Engng., 4, 177-183, 1999.
  • 8. D. S. HOWELL, B. V. TREADWELL, and S. B. TRIPPEL, Etiopathogenesis of osteoarthritis [In:] Osteoarthritis, Diagnosis and Medical/Surgical Management, R. W. MOSKOWITZ, D. S. HOWELL, V. M. GOLDBERG and V. C. HASKALL [Eds.], Raven Press, New York 1992.
  • 9. E. L. RADIN, R. B. MARTIN, D. B. BuRR, B. CATERSON, R. D. BOYD et al, Effects of mechanical loading on the tissues of the rabbit knee, J. Orthop. Res., 2, 221-234, 1984.
  • 10. J. J. TELEGA, Piezoelectricity and homogenization. Application to biomechanics [In:] Con­ tinuum Models and Discrete Systems, Vol. 2, G. A. MAUGIN [Ed.], 220-229, Longman, Essex 1991.
  • 11. W. Y. GU, W. M. LAI and V. C. MOW, Transport of fluid and ions through a porous­ permeable charged-hydrated tissue, and streaming potential data on normal bovine articular cartilage, J. Biomech., 26, 709-723, 1993.
  • 12. W. BIELSKI and J. J. TELEGA, Effective properties of geomaterials: rocks and porous media, Publications of Inst. of Geophysics Pol. Ac. Sci., Fasc. A-26 (285), Warsaw 1997.
  • 13. R. WOJNAR and J. J. TELEGA, Electrokinetics in dielectric porous media [In:] Problems of Environmental and Damage Mechanics, W. KOSIŃSKI, R. de BoER, D. GROSS, Wydawnictwa IPPT PAN, 97-136, Warszawa 1997.
  • 14. W. Y. GU, W. M. LAI and V. C. MOW, A mixture theory for charged-hydrated soft tissues containing multielectrolytes: passive transport and swelling behaviors, J. Biomech. Engng., 120, 169-180, 1998.
  • 15. A. J. GRODZINSKY, Electrochemical and physicochemical properties of connective tissue, CRC Critical Reviews in Biomed. Engng., 9, 133-199, 1983.
  • 16. A. GAŁKA, J. J. TELEGA and R. WOJNAR, Equations of electrokinetics and flow of electrolytes in porous media, J. Techn. Physics, 35, 49-59, 1994.
  • 17. J. J. TELEGA and R. WOJNAR, Flow of conductive fluids through poroelastic media with piezoelectric properties, J. Theor. App. Mech., 36, 775-794, 1998
  • 18. J. J. TELEGA and R. WOJNAR, Cartilage as an anisotropic multiphase material, Acta Bioneg. Biomech., 1, 499-502, 1999.
  • 19. J. J. TELEGA and R. WOJNAR, Flow of electrolyte through porous piezoelectric medium: macroscopic equations , C. R. Acad. Sci., 328, Sllrie lib, 225-230, Paris 2000.
  • 20. W. BIELSKI, J. J. TELEGA and R. WOJNAR, Macroscopic equations for nonstationary flow of Stokesian fluid through porous elastic medium, Arch. Mech., 51, 243-274, 1999.
  • 21. VAN C. MOW, A. RATCLIFFE and A. R. PooLE, Cartilage and diarthrodial joints as paradigms for hierachical materials and structures, Biomaterials, 13, 67-96, 1992.
  • 22. VAN C. MOW and A. RATCLIFFE, Structure and functions of articular cartilage and menis­ cus [In:] Basic Orthopaedic Biomechanics , V. C. MOW and W. C. HAYES [Eds.], Lippincott­ Raven Publishers, Philadelphia 1997.
  • 23. E. J. KUCHARZ, The collagens: Biochemistry and pathophysiology, Springer-Verlag, Berlin, 1992.
  • 24. G. MEACHIM and R. A. STOCKWELL, The matrix [In:] Adult articular cartilage, Second edition, M.A. R. FREEMAN [Eds.], Pitman Medical, Kent, UK 1979.
  • 25. P. M. COWAN, A. C. T. NORTH and J. T. RANDALL, X-ray diffraction studies of collagen fibres, Symp. Soc. Exp. Bioi., 9, 115-126, 1955.
  • 26. N. SASAKI and S. ODAJIMA, Stress-strain curoe and YOUNG's modulus of a collagen molecule as determined by the X-ray diffraction technique, J. Biomech., 29, 655-658, 1996.
  • 27. J. P. G. URBAN, The chondrocyte: a cell under pressure, Br. J. Rheumatol., 33, 901-908, 1994.
  • 28. V. C. MOW, A. RATCLIFFE, M.P. ROSENWASSER and J. A. BUCKWALTER, Experimental studies on repair of large osteochondral defects at a high weight bearing area of the knee joint: a tissue enegineering study, J. Biomech. Engng., 113, 198-207, 1991.
  • 29. M. T. DE WITT, C. J. Handley, B. W. OOCHES and D. A. LOWTHER, In vitro response to mechanical loading. The effect of a short term mechanical tension, Commt. Tiss. Res., 12, 97-109, 1984.
  • 30. F. GUILAK , Compression-induced changes in the shape and volume of the chondrocyte nucleus, J. Biomech., 28, 1529-1542, 1995.
  • 31. W. R. JONES, H. P. TING-BEALL, G. M. LEE, S. S. KELLEY, R. M. HOCHMUTH and F. GuiLAK, Mechanical properties of human chondrocytes and chondrons from normal and osteoarthritic cartilage, Trans. Orthop. Res. Soc., 22, 199, 1997.
  • 32. D. SHIN and K. A. ATHANASIOU, Biomechanical properties of the individual cell, Trans. Orthop. Res. Soc., 22, 352, 1997.
  • 33. J. Z. Wu, W. HERZOG and M. EPSTEIN, Modelling of location- and time-dependent deformation of chondrocytes during cartilage loading, J. Biomech., 32, 563-572, 1999.
  • 34. R. W. ZIMMERMANN, Elastic moduli of solid containing spherical inclusions, Mech. Material, 12, 17-24, 1991.
  • 35. R. L. SMITH, B. S. DONLIN, M. K. GUPTA, M. MOHTAI, P. DAS, D. R. CARTER, J. COOKE, G. GiBBONS, N. HUTCHINSON and D. J. SHURMAN, Effect of fluid - induced shear on articular chondrocyte morphology and metabolism in vitro, J. Orthop. Res., 13, 824-831, 1995.
  • 36. W. M. LAI, J. S. HOW , and V. C. MOW, A triphasic theory for the swelling and deformation behaviors of articular cartilage, J. Biomech. Engng., 113, 245-258, 1991.
  • 37. F. G. DONNAN, The theory of membrane equilibria, Chemical Rev., 1, 73-90, 1924.
  • 38. VAN C. MOW, M. H. HOLMES and W. M. LAI, Fluid transport and mechanical properties of articular cartilage: a review, J. of Biomech., 17, 377-394, 1984.
  • 39. J. M. OWENS, W. M. LAI and V. C. MOW, Biomechanical effects due to Na+ and Ca 2+exchange in articular cartilage, Trans. Orthop. Res. Soc., 16, 360, 1991.
  • 40. W. Y. Gu, W. M. LAI and V. C. MOW, A mixture theory for charged hydrated soft tissues containing multi-electrolytes: passive transport and swelling behaviors, J. Biomech. Engng., 120, 169-180, 1998.
  • 41. Y. LANIR, J. SEYBOLD, R. ScHNEIDERMAN and J. M. HUYGHE, Partition and diffusion of sodium and chloride ions in soft charged foam: the effect of external salt concentration and mechanical deformation, Tissue Engng., 4, 365-378, 1998.
  • 42. A. J. H. FRIJNS, J. M. HUYGHE and J.D. JANSSEN, A validation of the quadriphasic mixture theory for intervertebral disc tissue, Int. J. Engng Sci., 35, 1419-1429, 1998.
  • 43. J. M. HUYGHE and J. D. JANSSEN, Thermo-chemo-electro-mechanical formulation of saturated charged porous solids, Transport in Porous Media, 34, 129-141, 1999.
  • 44. J. M. HUYGHE, Intra-extrafibrillar mixture formulation of soft charged hydrated tissues, J. Theor. App. Mech., 37, 519-536, 1999.
  • 45. L. D. LANDAU and E. M. LIFSHITZ, Electrodynamics of continuous media (in Russian), Gosud. Izd. Tekhn. Teoret. Literat., Moskva 1957.
  • 46. E. M. LIFSHITS, L. D. PITAYEVSKIY, Physical kinetics (in Russian), Nauka, Moskva 1979.
  • 47. M. SUFFCZYNSKI , Elektrodynamika, PWN, Warszawa 1980.
  • 48. R. J. HUNTER, Zeta potential in colloid science, Academic Press, London 1981.
  • 49. A. TESO, A. D. FILHO and A. A. NETO, Solution of the Poisson-Boltzmann equation for a system with four ionic species, J. Math. Biol., 35, 814-824, 1997.
  • 50. R. UKLEJEWSKI, Electromechanical potentials in a fluid-filled cortical bone: initial stress state in osteonic lamellae, piezoelectricity and streaming potential roles - a theory, Biocy­ bernetics and Biomedical Engng., 13, 97-112, 1993.
  • 51. R. UKLEJEWSKI, Initial piezoelectric polarization of cortical bone matrix as a determinant of the electrokinetic potential Zeta of the bone osteonic lamellae as mechanoelectret, J. Biomechanics, 27, 339-360, 1994.
  • 52. G. ALLAIRE, Homogenization of the Stokes flow in a connected porous medium, Asymptotic Anal., 2, 203-222, 1989.
  • 53. G. ALLAIRE, Continuity of the Darcy's law in the low-volume fraction limit, Annali Scuola Norm. Sup. Pisa, Sci. Fis. e Mat., Ser. IV, 18, 475-499, 1991.
  • 54. J. L. AURIAULT and E. SANCHEZ-PALENCIA, Etude du comportement macroscopique d'un milieu poreux sature deformable, J. Mec., 16, 575-603, 1977.
  • 55. J. L. AURIAULT and T. STRZELECKI, On the electro-osmotic flow in a saturated porous medium, Int. J. Engng. Sci., 19, 915-928, 1981.
  • 56. A. GAŁKA, J. J. TELEGA and R. WOJNAR, Homogenization and thermo-piezoelectricity, Mech. Res. Comm., 19, 315-324, 1992.
  • 57. A. BENSOUSAN, J.-L. LIONS and G. PAPANICOLAOU, Asymptotic analysis of periodic structures, North-Holland, Amsterdam 1978.
  • 58. T. LEWINSKI, J. J. TELEGA, Plates, laminates and shells: Asymptotic analysis and homogenization, World Scientific, Singapore 2000.
  • 59. N.D. BROOM and D. L. MARRA, New structural concepts of articular cartilage demonstrated with a physical model, Connect. Tiss. Res., 14, 1-8, 1985.
  • 60. N. D. BROOM, Connective tissue function and malfunction: a biomechanical perspective The Third George Swanson Christie Memorial Lecture Pathology, 20, 93-104, 1988.
  • 61. A. GAŁKA, J. J. TELEGA, S. TOKARZEWSKI, Effective moduli for a trabecular bone wit regular microstructure, Acta Bioeng. Biomech., 2, Suplement 1, 555-560, 2000.
  • 62. L. J. GIBSON, M. F. ASHBY, Cellular solids, structure and properties, Pergamon Press, OxFORD 1988.
  • 63. S. JEMIOŁO and J. J. TELEGA, Isotropic and transversaly isotropic hyperelastic models o soft tissues, Part 1.& II, Engng. Trans., 49, 2-3, 2001.
  • 64. Y. C. FUNG, Biomechanics: mechanical properties of living tissues, Springer Verlag, New York 1993
  • 65. S. JEMIOŁO and J. J. TELEGA, On modelling transversally isotropic materials Udergoin large deformations and application to modelling soft tissues, Mech. Res. Comm., submitted
  • 66. J. J. TELEGA, A. GAŁKA and S. TOKARZEWSKI, Application of reiterated homogenizatio to determination of effective moduli of a compact bone, J. Theor. Appl. Mech., 37, 687-706 1999.
  • 67. A. GAŁKA, J. J. TELEGA and R. WOJNAR, Macroscopic elastic properties of cartilage, Act Bioeng. Biomech., 2, Suplement 1, 187-192, 2000.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPB2-0004-0074
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