Trabecular Bone Poroelasticity for MicroCT-Based FE Models

  • Clara Sandino
  • Steven K. Boyd
Conference paper


A useful mathematical model that describes the mechanical behavior of bone is the poroelastic model. So far, numerical studies of trabecular bone poroelasticity have considered the tissue as a homogeneous porous structure. The objective of this study was to develop a methodology for creating large-scale finite element models that predict the poroelastic response of trabecular bone, including the tissue micro-architecture. 1 cm3 cubes of bovine trabecular bone were scanned using micro-computed tomography. Finite elements models were developed using different voxel and sample sizes. Strain equivalent to 1% of deformation was applied at three different rates and confined and unconfined conditions were simulated. Stress distributions in the bone phase were similar under confined and unconfined conditions. The fluid velocity and the pore pressure in the marrow were higher under confined than under unconfined conditions. The trabecular bone stiffness was higher under confined compared to under unconfined conditions, increasing with increments in the strain rate. Variations in the sample size were more significant in the predicted stiffness than variations in the voxel size. This study included both the poroelasticity and the micro-architecture of trabecular bone to predict changes in the mechanical response of trabecular tissue under time-dependent loading conditions.


Pore Pressure Trabecular Bone Voxel Size Pore Volume Fraction Biomechanical Response 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



Dr. Dennis Coombe is acknowledged for some discussions. This work was supported by funding from the Natural Science and Engineering Research Council of Canada and Alberta Innovates-Health Solutions.


  1. 1.
    Anderson, C.B.: In: Baumeister, T. (ed.) Marks’ Standard Handbook for Mechanical Engineers, pp. 3.48–3.76. MacGraw-Hill, New York (1967)Google Scholar
  2. 2.
    Biot, M.A.: General theory of three-dimensional consolidation. J. Appl. Phys. 12, 155–164 (1941)MATHCrossRefGoogle Scholar
  3. 3.
    Caplan, A.I.: Mesenchymal stem cells. J. Orthop. Res. 9, 641–650 (1991)CrossRefGoogle Scholar
  4. 4.
    Carter, D.R., Hayes, W.C.: The compressive behavior of bone as a two-phase porous structure. J. Bone Joint Surg. Am. 59, 954–962 (1977)Google Scholar
  5. 5.
    Cowin, S.C.: Bone poroelasticity. J. Biomech. 32, 217–238 (1999)CrossRefGoogle Scholar
  6. 6.
    Johnson, M.W., Chakkalakal, D.A., Harper, R.A., Katz, J.L., Rouhana, S.W.: Fluid flow in bone in vitro. J. Biomech. 15, 881–885 (1982)CrossRefGoogle Scholar
  7. 7.
    Lacroix, D., Prendergast, P.J.: A mechano-regulation model for tissue differentiation during fracture healing: analysis of gap size and loading. J. Biomech. 35, 1163–1171 (2002)CrossRefGoogle Scholar
  8. 8.
    Lim, T.H., Hong, J.H.: Poroelastic properties of bovine vertebral trabecular bone. J. Orthop. Res. 18, 671–677 (2000)CrossRefGoogle Scholar
  9. 9.
    Linde, F., Norgaard, P., Hvid, I., Odgaard, A., Soballe, K.: Mechanical properties of trabecular bone. Dependence on strain rate. J. Biomech. 24, 803–809 (1991)Google Scholar
  10. 10.
    Muller, R., Hildebrand, T., Ruegsegger, P.: Non-invasive bone biopsy: a new method to analyze and display the three-dimensional structure of trabecular bone. Phys. Med. Biol. 39, 145–164 (1994)CrossRefGoogle Scholar
  11. 11.
    Nauman, E.A., Fong, K.E., Keaveny, T.M.: Dependence of intertrabecular permeability on flow direction and anatomic site. Ann. Biomed. Eng. 27, 517–524 (1999)CrossRefGoogle Scholar
  12. 12.
    Schaffler, M.B., Burr, D.B.: Stiffness of compact bone: effects of porosity and density. J. Biomech. 21, 13–16 (1988)CrossRefGoogle Scholar
  13. 13.
    Smit, T.H., Huyghe, J.M., Cowin, S.C.: Estimation of the poroelastic parameters of cortical bone. J. Biomech. 35, 829–835 (2002)CrossRefGoogle Scholar
  14. 14.
    van Rietbergen, B., Majumdar, S., Pistoia, W., et al.: Assessment of cancellous bone mechanical properties from micro-FE models based on micro-CT, pQCT and MR images. Technol. Health Care 6, 413–420 (1998)Google Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Schulich School of EngineeringUniversity of CalgaryCalgaryCanada
  2. 2.Roger Jackson Centre for Health and Wellness ResearchUniversity of CalgaryCalgaryCanada
  3. 3.McCaig Institute for Bone and Joint HealthUniversity of CalgaryCalgaryCanada

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