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Tissue Adaptation as a Discrete-Dynamical Process in Time and Space

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IUTAM Symposium on Synthesis in Bio Solid Mechanics

Part of the book series: Solid Mechanics and its Applications ((SMIA,volume 69))

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References

  1. Hooke, R. (1664) Micrographia. Or Some Physiological Descriptions Of Minute Bodies Made By Magnifying Glass With Observations And Inquiries Thereupon. Royal Society: London. Facsimile Edition, Science Heritage Limited: Lincolnwood, Illinois, 1987.

    Google Scholar 

  2. Owen, M.(1980) The origin of cells in the postnatal organism, Arthritis and Rheumatism 23, 1073–1079.

    Google Scholar 

  3. Caplan, AI. (1994) The mesengenic process, Clinics in Plastic Surgery 21, 429–435.

    CAS  Google Scholar 

  4. Wolpert, L. (1989) Positional information revisited, Development Suppl. 3–12.

    Google Scholar 

  5. Huiskes, R. (1997) Simulation of self-organization and functional adaptation in bone, in E. Schneider (ed.), Biomechanik des menschlichen Bewegung sapparates. Springer-Verlag, Berlin, pp. 299–320.

    Google Scholar 

  6. Singer, C. (1959) A History of Scientific Ideas. Oxford University Press.

    Google Scholar 

  7. Roux, W. (1912) Anpassungslehre, Histomechanik und Hostochemie, Virchows Archiv, 207, 168–209.

    Google Scholar 

  8. Weinans, H. and Prendergast, P.J. (1996) Tissue adaptation as a dynamical process far from equilibrium, Bone 19, 143–149.

    CAS  Google Scholar 

  9. Turing, A. M. (1952) The chemical basis of morphogenesis, Proc. Roy. Soc. (Lond.) 237, 37–72.

    Google Scholar 

  10. Cowin S.C., Moss-Salentijn, L. and Moss, M.L. (1991) Candidates for the mechanosensory system in bone, ASME J. Biomech. Eng. 113, 191–197.

    CAS  Google Scholar 

  11. Prendergast, P.J. and Huiskes, R. (1996) Microdamage and osteocyte-lacuna strain in bone: A microstructural finite element analysis, J. Biomech. Eng. 118, 240–246.

    CAS  Google Scholar 

  12. Cooke, J. and Zeeman, E.C. (1976) A clock and wavefront model for control of the number of repeated structures during animal morphogenesis, J. Theor. Biol. 58, 455–476.

    CAS  Google Scholar 

  13. Brand, R.A. (1992) Autonomous informational stability in connective tissues, Medical Hypothesis 37, 107–114.

    CAS  Google Scholar 

  14. Klein-Nulend, J., Semeins, C.M., Burger, E.H., van der Plas, A., Ajubi, N.E. and Nijweide, P.J. (1996) Response of isolated osteocytes to mechanical loading in vitro, in A. Odgaard. and H. Weinans (eds.), Bone Structure and Remodelling. World Scientific: Singapore, pp. 37–49.

    Google Scholar 

  15. Lanyon, L.E. (1993) Osteocytes, strain detection, bone modelling and remodelling, Calcif: Tissue Int. 53(Suppl): S102–107.

    Google Scholar 

  16. Cowin S.C., Arramon Y.P., Luo, G.M. and Sadegh AM. (1993) Chaos in the discrete-time algorithm for bone density remodelling rate equations. J. Biomech. 26, 1077–90.

    CAS  Google Scholar 

  17. Smale, S. (1974) A mathematical model of two cells via Turing’s equation, Lectures on Mathematics in the Life Sciences 6, 16–26.

    Google Scholar 

  18. Sigmund, O. (1994) Design of Material Structures Using Topology Optimization. Danish Centre for Applied Mathematics and Mechanics: Lygby.

    Google Scholar 

  19. Weinans, H., Huiskes, R. and Grootenboer, H.J. (1992) The behaviour of adaptive bone remodelling simulation models, J. Biomech. 25, 1425–1441.

    Article  CAS  Google Scholar 

  20. Mullender, M.G., Huiskes, R. and Weinans, H. (1994) A physiological approach to the simulation of bone remodelling as a self-organisational control process, J. Biomech 27, 1389–1394.

    Article  CAS  Google Scholar 

  21. Jacobs, C.R., Levenston, M.E., Beaupré, G.S., Simo, J.C. and Carter, D.R. (1995) Numerical instabilities in bone remodelling simulations: The advantages of a node-based finite element approach. J. Biomech. 28, 449–459.

    Article  CAS  Google Scholar 

  22. May, R.M. (1976) Simple mathematical models with very complicated dynamics. Nature 261, 459–467.

    Article  CAS  Google Scholar 

  23. Nicolis, G. and Prigogine, I. (1977) Self-Organisation in Non-Equilibrium Systems. From Dissipative Systems to Order Through Fluctuations. New York: Wiley.

    Google Scholar 

  24. Prendergast, P.J. (1997) Stable, periodic, and chaotic solutions for damage adaptive remodelling. Trans. Euro. Orthop. Res. Soc. 7, p. 65.

    Google Scholar 

  25. Capra, F. (1982) The Turning Point. Science, Society and the Rising Culture. Flamingo: London. p. 304

    Google Scholar 

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© 1999 Kluwer Academic Publishers

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Prendergast, P.J., Weinans, H. (1999). Tissue Adaptation as a Discrete-Dynamical Process in Time and Space. In: Pedersen, P., Bendsøe, M.P. (eds) IUTAM Symposium on Synthesis in Bio Solid Mechanics. Solid Mechanics and its Applications, vol 69. Springer, Dordrecht. https://doi.org/10.1007/0-306-46939-1_28

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  • DOI: https://doi.org/10.1007/0-306-46939-1_28

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-0-7923-5615-8

  • Online ISBN: 978-0-306-46939-8

  • eBook Packages: Springer Book Archive

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