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Torsional rigidities of cancellous bone filled with marrow : the application of multipoint Padé approximants

Wybrane pełne teksty z tego czasopisma
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
An idealized model of prism-like trabecular bone was developed to study its static and dynamic responses under torsional moments. Effects of bone marrow and bone apparent density were investigated. By constructing multipoint Padé approximants [1-2] to the torsional complex modulus, hydraulic stiffening of the prism-like bone due to the presence of bone marrow was predicted. The torsional compliance, creep function and relaxation function were also evaluated.
Słowa kluczowe
Rocznik
Strony
135--153
Opis fizyczny
Bibliogr. 35 poz., tab., wykr.
Twórcy
  • Institute of Fundamental Technological Research Polish Academy of Sciences Świętokrzyska 21, 00-049 Warsaw, Poland
autor
  • Institute of Fundamental Technological Research Polish Academy of Sciences Świętokrzyska 21, 00-049 Warsaw, Poland
autor
  • Institute of Fundamental Technological Research Polish Academy of Sciences Świętokrzyska 21, 00-049 Warsaw, Poland
Bibliografia
  • 1. G. A. BAKER, Best error bounds for Pade approximants to convergent series of Stieltjes, J. Math. Phys., 10, 814-820, 1969.
  • 2. G. A. BAKER, P. GRAVES-MORRIS, Pade Approximants, Second Edition, GIAN-CARLO RoTA, [Eds.], [In:] Encyclopedia of Mathematics and its Applications, 59, Cambridge University Press, Cambridge 1996.
  • 3. G. S. BEAUPRE, W. C. HAYES, Finite element analysis of a three dimensional opened-celled model for trabecular bone, J. Biomech. Engng., 107, 249-256, 1985.
  • 4. A. BENSOUSSAN, J. L. LIONS, G. PAPANICOULAOU, Asymptotic analysis for periodic structures, North- Holland, Amsterdam 1978.
  • 5. D. R. CARTER, W. C. HAYES, The compressive behaviour of bone as a two-phase porous structure, J. Bone Jt. Surg., 59A, 954-962, 1977.
  • 6. R. M. CHRISTENSEN, Mechanics of composite materials, John Wiley&Sons, New York 1979.
  • 7. D. CIORANESCU, J. SAINT JEAN PAULIN, Homogenization of reticulated structures, Springer­Verlag, New York 1999.
  • 8. D. CIORANESCU, J. SAINT JEAN PAULIN, Asymptotic analysis of elastic wireworks, Laboratoire d'analyse numerique, R89008, Universite Paris 1989.
  • 9. N. L. FAZZALARI, J. DARRACOTT, B. VERNON-ROBERTS, Histomorphometric changes in the trabecular structure of a selected stress region in the femur in patiens with osteoarthritis and fracture of the femoral neck, Bone, 6, 125-133, 1985.
  • 10. J. L. GIBSON, The mechanical behaviour of cancellous bone, J. Biomechanics, 18, 317-328, 1985.
  • 11. L. J. GIBSON, M. F. ASHBY, Cellular solids: structure and properties, Pergamon Press, New York 1988.
  • 12. K. GOLDEN and G. PAPANICOLAOU, Bounds for effective parameters of heterogeneous media by analytic continuation, Comm. Math. Phys., 90, 473--491, 1983.
  • 13. X. E. GUO, T. A. McMAHON, T. M. KEAVENY, W. C. HAYES, L. GIBSON, Finite modelling damage accumulation in trabecular bone under cycling loading, J. Biomechanics, 27, 145-155, 1994.
  • 14. T. P. HARRIGAN, M. JASNY, R. W. MANN, W. H. HARRIS, Limitation of the continuum assumption in cancellous bone, J. Biomechanics, 21, 269-275, 1988.
  • 15. S. J. HOLLISTER, D. P. FYHIRE, K. J. JEPSEN, S. A. GOLDSTEIN, Application of homogenization theory to the study of trabecular bone mechanics, J. Biomechanics, 24, 825-839, 1991.
  • 16. M. KASRA, M. D. GRYNPAS, Static and dynamic finite element analyses of an idealized structural model of vertebral trabecular bone, J. Biomech. Engng., 120, 267-272, 1998.
  • 17. R. B. MARTIN, D. B. BURR, N. A. SHARKEY, Skeletal Tissue Mechanics, Springer-Verlag, New York 1998.
  • 18. J. McELHANEY, N. ALEM, V. ROBERTS, A porous block model for cancellous bones, ASME Publication No 70-WA/BHF-2, 1-9, 1970.
  • 19. N. I. MUSHELISHVILI, Some basic problems of mathematical theory of elasticity [in Russian], Nauka, Moskva 1966.
  • 20. R. MOLLER, P. ROEGSEGGER, Micro-tomographic imaging for the nondestructive evaluation of trabecular bone architecture, [In:] Bone Research in Biomechanics, G. LowET, P. ROEGSEGGER, H. WEINANS and A. MEUNIER [Eds.], 61-79, lOS Press, Amsterdam 1997.
  • 21. J. A. OCHOA, D. A. HECK, K. D. BRANDT, B. M. HILLBERRY, The effect of intertrabecular fluid on femoral head mechanics, J. of Reumatology, 18, 580-584, 1991.
  • 22. J. SAINT, J. PAULIN, Developpement asymptotique et calcul de correcteures pour la torsion elastique d'arbres a cavites cylindriques, Report No 78021, Analyse Numerique Universite Pierre et Marie Curie, 1978.
  • 23. W. T. PERRINS, D. R. McKENZIE, R. C. Me PHEDRAN, Transport properties of regular array of cylinders, Proc. R. Soc. Lond., A 369, 207-225, 1979.
  • 24. J. W. UuGH, R. M. ROSE, E. L. RADIN, A structural model for the mechanical behavior of trabecular bone, J. Biomechanics, 6, 657-670, 1973.
  • 25. E. SANCHEZ-PALENCIA, Non-homogeneous media and vibration theory, Springer, Berlin 1980.
  • 26. M. TAVASSOLI, J. M. YOFFEY, Bone marrow: structure and function, Alan R. Liss, New York 1983.
  • 27. J. TELEGA, A. GAŁKA, S. TOKARZEWSKI, Effective moduli of trabecular bone, Acta Bioeng. Biomech., 1, 53-57, 1999.
  • 28. J. J. TELEGA, A. GAŁKA, S. TOKARZEWSKI, Application of the reiterated homogenization to determination of effective moduli of a compact bone, J. Theor. Appl. Mech., 37, 687-706, 1999.
  • 29. J. J. TELEGA, T. LEKSZYCKI, Progress in functional adaptation of tissues and remodelling, Part I. Bone structure, its properties and models, Engng. Trans., (in preparation).
  • 30. S. TOKARZEWSKI, N-point Pade approximants to real-valued Stieltjes series with nonzero radii of convergence, J. Comp. Appl. Math., 75, 259-280, 1996.
  • 31. S. TOKARZEWSKI and J. J. TELEGA, S-continued fraction method for the investigation of a complex dielectric constant of two-phase composite, Acta Appl. Math., 49, 55-83, 1997.
  • 32. S. TOKARZEWSKI, J. J. TELEGA, Bounds on efffective moduli by analytical continuation of the Stieltjes function expanded at zero and infinity, Z. angew. Math. Phys., 48, 1-20, 1997.
  • 33. S. TOKARZEWSKI, J. J. TELEGA, A. GAŁKA, A contribution to evaluation of effective moduli of trabecular bone with rod-like microstructure, J. Theor. Appl. Mech., 37, 3, 707-728, 1999.
  • 34. R. S. WEINSTEIN, M.S. HUTSON, Decreased trabecular width and increased trabecular spacing contribute to loss with aging, Bone, 8, 137-142, 1987.
  • 35. J. L. WILLIAMS, J. L. LEWIS, Properties and anisotropic model of cancellous bone from the proximal tibia epiphysis, J. Biomech. Engng., 104, 50-56, 1982
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPB2-0004-0067
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