Medical Engineering & Physics
Volume 30, Issue 6 , Pages 725-732 , July 2008

Predicting trabecular bone microdamage initiation and accumulation using a non-linear perfect damage model

  • Victor Kosmopoulos

      Affiliations

    • Hôpital Orthopédique de la Suisse Romande, Avenue Pierre-Decker 4, CH-1005 Lausanne, Switzerland
    • Corresponding Author InformationCorresponding author. Tel.: +41 215450329.
    • ,
  • Tony S. Keller

      Affiliations

    • Musculoskeletal Research Foundation, Tampa, FL, United States
    • Dr. Tony S. Keller's life was tragically taken on 6 December 2006, just about half a month after this manuscript was submitted. Tony was a bright and energetic researcher, an outstanding teacher and mentor, and a beloved friend. He will be greatly missed.

Received 13 November 2006 ,Revised 16 February 2007 ,Accepted 16 February 2007.

References 

  1. Bentolila V, Boyce TM, Fyhrie DP, Drumb R, Skerry TM, Schaffler MB. Intracortical remodeling in adult rat long bones after fatigue loading. Bone. 1998;23:275–281
  2. Martin RB, Burr DB. A hypothetical mechanism for the stimulation of osteonal remodelling by fatigue damage. J Biomech. 1982;15:137–139
  3. Pugh JW, Rose RM, Radin EL. A possible mechanism of Wolff's law: trabecular microfractures. Arch Int Physiol Biochim. 1973;81:27–40
  4. Jepsen KJ, Davy DT. Comparison of damage accumulation measures in human cortical bone. J Biomech. 1997;30:891–894
  5. Carter DR, Hayes WC. The compressive behavior of bone as a two-phase porous structure. J Bone Joint Surg Am. 1977;59:954–962
  6. Jepsen KJ, Davy DT, Akkus O. Observations of damage in bone. In:  Cowin SC editors. Bone mechanics handbook. Boca Raton: CRC Press; 2001;p. 17.1–17.12
  7. Keller TS. Predicting the compressive mechanical behavior of bone. J Biomech. 1994;1159–1168
  8. Kopperdahl DL, Roberts AD, Keaveny TM. Localized damage in vertebral bone is most detrimental in regions of high strain energy density. J Biomech Eng. 1999;121:622–628
  9. Pidaparti RM, Liu Y. Bone stiffness changes due to microdamage under different loadings. Bio-Med Mater Eng. 1997;7:193–203
  10. Taylor M, Verdonschot N, Huiskes R, Zioupos P. A combined finite element method and continuum damage mechanics approach to simulate the in vitro fatigue behavior of human cortical bone. J Mater Sci Mater Med. 1999;10:841–846
  11. Guo XE, McMahon TA, Keaveny TM, Hayes WC, Gibson LJ. Finite element modeling of damage accumulation in trabecular bone under cyclic loading. J Biomech. 1994;27:145–155
  12. Makiyama AM, Vajjhala S, Gibson LJ. Analysis of crack growth in a 3D Voronoi structure: a model for fatigue in low-density trabecular bone. J Biomech Eng. 2002;124:512–520
  13. Schaffner G, Guo XE, Silva MJ, Gibson LJ. Modeling fatigue damage accumulation in two-dimensional Voronoi honeycombs. Int J Mech Sci. 2000;42:645–656
  14. Fyhrie DP, Hou FJ. Prediction of human vertebral cancellous bone strength using non-linear, anatomically accurate, large-scale, finite element analysis.. Trans ASME BED. 1995;29:301–302
  15. Keller TS, Kosmopoulos V, Lieberman IH, Vertebroplasty . Kyphoplasty affect vertebral motion segment stiffness and stress distributions: a microstructural finite-element study. Spine. 2005;30:1258–1265
  16. Kosmopoulos V, Keller TS. Finite element modeling of trabecular bone damage. Comp Methods Biomech Biomed Eng. 2003;6:209–216
  17. Kosmopoulos V, Keller TS. Damage-based finite-element vertebroplasty simulations. Eur Spine J. 2004;13:617–625
  18. Niebur GL, Feldstein MJ, Yuen JC, Chen TJ, Keaveny TM. High-resolution finite element models with tissue strength asymmetry accurately predict failure of trabecular bone. J Biomech. 2000;33:1575–1583
  19. van Rietbergen B, Pistoia W, Ulrich D, Huiskes R, Ruegsegger P. Prediction of trabecular bone failure parameters using a tissue failure criterion and μFE analysis. Comp Simul Modell Med. 2000;1:98–101
  20. Betten J. Generalization of nonlinear material laws found in experiments to multi-axial states of stress.. Eur J Mech A Solids. 1989;8:325–339
  21. Kosmopoulos V, Keller TS, Baroud G, Steffen T. Experimental and numerical simulation of microdamage and failure of thoracic vertebral trabecular bone. Trans Orthop Res Soc. 2003;453
  22. Saxena R, Keller TS, Sullivan JM. A three-dimensional finite element scheme to investigate the apparent mechanical properties of trabecular bone. Comp Methods Biomech Biomed Eng. 1999;2:285–294
  23. Suwito W, Keller TS, Basu PK, Weisberger AM, Strauss AM, Spengler DM. Geometric and material property study of the human lumbar spine using the finite element method. J Spinal Disord. 1992;5:50–59
  24. Keller TS, Kosmopoulos V, Liebschner MAK. Modeling of bone damage and fracture in osteoporosis. In:  Szpalski M,  Gunzburg R editor. Vertebral osteoporotic compression fractures. Philadelphia: Lippincott Williams & Wilkins; 2003;p. 35–50
  25. Lode W. Versuche uber den Einfluss der mittleren Hauptspannung auf das fliessen des Matalle Eisen, Kaupfer, and Nickel. Z Phys. 1926;36:913
  26. Kachanov LM. Introduction to continuum damage mechanics. Dordrecht: Martinus Nijhoff Publishers; 1986;
  27. Lemaitre J. A course on damage mechanics. Berlin: Springer-Verlag; 1992;
  28. Burr DB, Forwood MR, Fyhrie DP, Martin RB, Schaffler MB, Turner CH. Bone microdamage and skeletal fragility in osteoporotic and stress fractures. J Bone Miner Res. 1997;12:6–15[Review] [67 refs]
  29. Burr DB, Martin RB, Schaffler MB, Radin EL. Bone remodeling in response to in vivo fatigue microdamage. J Biomech. 1985;18:189–200
  30. Martin B. Mathematical model for repair of fatigue damage and stress fracture in osteonal bone. J Orthop Res. 1995;13:309–316
  31. Stolken JS, Kinney JH. On the importance of geometric nonlinearity in finite-element simulations of trabecular bone failure. Bone. 2003;33:494–504[see comment]
  32. Kosmopoulos V, Keller TS. Non-uniform loading results in increased trabecular bone microfracture. Trans Orthop Res Soc. 2005;126
  33. Wachtel EF, Keaveny TM. Dependence of trabecular damage on mechanical strain. J Orthop Res. 1997;15:781–787
  34. Bourne BC, van der Meulen MC. Finite element models predict cancellous apparent modulus when tissue modulus is scaled from specimen CT-attenuation. J Biomech. 2004;37:613–621
  35. Turner CH, Rho J, Takano Y, Tsui TY, Pharr GM. The elastic properties of trabecular and cortical bone tissues are similar: results from two microscopic measurement techniques. J Biomech. 1999;32:437–441
  36. Bayraktar HH, Adams MF, Gupta A, Papadopoulos P, Keaveny TM. The role of large deformations in trabecular bone mechanical behavior.. Trans ASME BED. 2003;31–32
  37. Bayraktar HH, Keaveny TM. Mechanisms of uniformity of yield strains for trabecular bone. J Biomech. 2004;37:1671–1678
  38. Morgan EF, Bayraktar HH, Yeh OC, Majumdar S, Burghardt A, Keaveny TM. Contribution of inter-site variations in architecture to trabecular bone apparent yield strain. J Biomech. 2004;37:1413–1420
  39. Keller TS, Kosmopoulos V. Finite element modeling of trabecular bone mechanical property degradation during cyclic loading. Trans Orthop Res Soc. 2005;118

PII: S1350-4533(07)00150-6

doi: 10.1016/j.medengphy.2007.02.011

Medical Engineering & Physics
Volume 30, Issue 6 , Pages 725-732 , July 2008

Article Tools

* Image Usage & Resolution