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A simplified theory of adaptive bone elastic beam buckling

  • Ramtani, Salah (Laboratoire CSPBAT-LBPS UMR 7244 CNRS Universite Paris-Nord, Institut Galilee) ;
  • Bennaceur, Hamza (Laboratoire Mecanique des Structures et Materiaux Universite de Batna, Departement de Mecanique, Faculte de technologie) ;
  • Outtas, Toufik (Laboratoire Mecanique des Structures et Materiaux Universite de Batna, Departement de Mecanique, Faculte de technologie)
  • Received : 2014.02.12
  • Accepted : 2014.09.30
  • Published : 2014.09.25
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Abstract

The usual assumption that the increase of fractures in aging bone is due entirely to lower bone density is taken back with respect to the possibility that aging bone fractures result from a loss of stability, or buckling, in the structure of the bone lattice. Buckling is an instability mode that becomes likely in end-loaded structures when they become too slender and lose lateral support. The relative importance of bone density and architecture in etiology bone fractures are poorly understood and the need for improved mechanistic understanding of bone failure is at the core of important clinical problems such as osteoporosis, as well as basic biological issues such as bone formation and adaptation. These observations motivated the present work in which simplified adaptive-beam buckling model is formulated within the context of the adaptive elasticity (Cowin and Hegedus 1976, Hegedus and Cowin 1976). Our results indicate that bone loss activation process leads systematically to the apparition of new elastic instabilities that can conduct to bone-buckling mechanism of fracture.

Keywords

References

  1. Bell, G.H. (1967), "Variations in strength of vertebrae with age and their relation to osteoporosis", Calcified. Tiss. Res., 1(1), 75-86. https://doi.org/10.1007/BF02008077
  2. Cowin, S.C. and Van Buskirk, W.C. (1978), "Internal bone remodeling induced by a medullary pin", J. Biomech., 11(5), 269-275. https://doi.org/10.1016/0021-9290(78)90053-2
  3. Cowin, S.C. and Hegedus, D.M. (1976), "Bone remodeling I : Theory of adaptive elasticity", J. Elasticity., 6(3), 313-325. https://doi.org/10.1007/BF00041724
  4. Frost, H.M. (1964), Laws of bone structure, Springfield, MA: Charles C Thomas.
  5. Goto, M., Kawakami, N., Azegami, H., Matsuyama, Y., Takeuchi, K. and Sasaoka, R. (2003), "Buckling and bone modeling as factors in the development of idiopathic scoliosis", Spine, 28(4), 364-70.
  6. Hasegawa, K., Turner, C.H., Recker, R.R., Wu, E. and Burr, D.B. (1995), "Elastic properties of osteoporotic bone measured by scanning acoustic microscopy", Bone, 16(1), 85-90. https://doi.org/10.1016/8756-3282(95)80016-J
  7. Hegedus, D.H. and Cowin, S.C. (1976), "Bone remodeling II: Small strain adaptive elasticity", J. Elasticity., 6(4), 337-352. https://doi.org/10.1007/BF00040896
  8. Ionovici, N., Negru, M., Grecu, D., Vasilescu, M., Mogoanta, L., Bold, A. and Traistaru, R. (2009), "Hypothesis of microfractures by buckling theory of bone's trabeculas from vertebral bodies affected by osteoporosis", Romanian. J. Morphol. Embryol., 50(1),79-84.
  9. Kanis, J.A., McCloskey, E., Johansson, H., Oden, A., Melton, L.J. and Khaltaev, N. (2008), "A reference standard for the description of osteoporosis", Bone, 42(3), 467-475. https://doi.org/10.1016/j.bone.2007.11.001
  10. Lee, T., Rammohan, A.V., Chan, A., Chye Tan, V.B., Das De, S. Link, T.M., Eckstein, F. and Schafer, B.W. (2012), "The susceptibility of the femoral neck to fracture: An assessment incorporating the effects of age-remodeling and stress reduction", J. Biomech., 45(6), 931-937. https://doi.org/10.1016/j.jbiomech.2012.01.021
  11. Lee, T., Choi, J.B., Schafer, B.W., Segars, W.P., Eckstein, F., Kuhn, V. and Beck, T.J. (2009), "Assessing the susceptibility to local buckling at the femoral neck cortex to age-related bone loss", Ann. Biomed. Eng., 37(9), 1910-1920. https://doi.org/10.1007/s10439-009-9751-9
  12. Lee, T.C., Noelke, L., McMahon, G.T., Mulville, J.P. and Taylor, D. (1998), "Functional adaptation in bone", Eds. P. Pedersen and M.P. Bendsoe, Synthesis in Bio Solid Mechanics, Kluwere Academic Publishers, Dortrecht.
  13. Lee, T., Schafer, B.W., Loveridge, N., Reeve, J. and Beck, T.J. (2005), "Finite strip analysis in the assessment of local buckling capacity of the femoral neck", Meeting of the Orthopedic Research Society,
  14. Washington, DC. Muller, R., Gerber, S.C. and Hayes, W.C. (1998), "Micro-compression: a novel method for the non-destructive assessment of bone failure", J. Biomech., 31, 150-150.
  15. Parker, A. (2006), "A new look at how aging bones fracture", Sci. Tech. Rev., UCRL-TR-52000-06-9 Distribution Category UC-99 September, 20-21.
  16. Ramtani, S. and Abdi, M. (2005), "Buckling of adaptive elastic bone-plate: theoretical and numerical investigation", Biomech. Model. Mechanobiol., 3(4), 200-208. https://doi.org/10.1007/s10237-004-0056-5
  17. Recker, R.R. (2007), "Skeletal fragility and bone quality", J. Musculoskelet. Neuronal Interact., 7, 54-55.
  18. Saha, G. and Banu, S. (2007), "Buckling load of beam column for different end conditions using multisegment integration technique", ARPN, J. Eng. Appl. Sci., 2(1), 27-32.
  19. Selby, P.L., Davie, M.W.J., Ralston, S.H. and Stone, M.D. (2002), "Guidelines on the management of Paget's disease of bone", Bone, 31(3), 10-19.
  20. Vinson, J.R. (1989), "The behavior of thin walled structures-Beams, plates, and shells", Dordrecht etc., Kluwer Academic Publishers.
  21. Warwar, R.E., Bullock, J.D., Ballal, D.R. and Ballal, R.D. (1999), "Mechanisms of orbital floor fractures: A clinical, experimental, and theoretical study", Trans. Am. Ophthalmol. Soc., 97, 87-113.

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