Classification and visualization of primary trabecular bone in lumbar vertebrae

  • Received : 2013.09.11
  • Accepted : 2014.05.14
  • Published : 2014.04.25


The microarchitecture of trabecular bone plays a significant role in mechanical strength due to its load-bearing capability. However, the complexity of trabecular microarchitecture hinders the evaluation of its morphological characteristics. We therefore propose a new classification method based on static multiscale theory and dynamic finite element method (FEM) analysis to visualize a three-dimensional (3D) trabecular network for investigating the influence of trabecular microarchitecture on load-bearing capability. This method is applied to human vertebral trabecular bone images obtained by micro-computed tomography (micro-CT) through which primary trabecular bone is successfully visualized and extracted from a highly complicated microarchitecture. The morphological features were then analyzed by viewing the percolation of load pathways in the primary trabecular bone by using the stress wave propagation method analyzed under impact loading. We demonstrate that the present method is effective for describing the morphology of trabecular bone and has the potential for morphometric measurement applications.



Supported by : Ministry of Higher Education (MOHE)


  1. Andrade Silva, F., Williams, J.J., Muller, B.R., Hentschel, M.P., Portella, P.D. and Chawla, N. (2010), "Three-dimensional microstructure visualization of porosity and Fe-rich inclusions in SiC particlereinforced Al alloy matrix composites by X-Ray synchrotron tomography", Metall. Mater. Trans. A, 41(8), 2121-2128.
  2. Basaruddin, K.S., Takano, N., Akiyama, H. and Nakano, T. (2013), "Uncertainty modeling in the prediction of effective mechanical properties using stochastic homogenization method with application to porous trabecular bone", Mater. Trans., 54(8), 1250-1256.
  3. Basaruddin, K.S., Takano, N. and Nakano, T. (2013), "Stochastic multi-scale prediction on the apparent elastic moduli of trabecular bone considering uncertainties of biological apatite (BAp) crystallite orientation and image-based modeling", Comput. Methods Biomech. Biomed. Eng. doi: 10.1080/10255842.2013.785537.
  4. Blain, H., Chavassieux, P., Portero-Muzy, N., Bonnel, F., Canovas, F., Chammas, M., Maury, P. and Delmas, P.D. (2008), "Cortical and trabecular bone distribution in the femoral neck in osteoporosis and osteoarthritis", Bone, 43(5), 862-868.
  5. Gefen, A. (2009). Finite Element Modeling of the Microarchitecture of Cancellous Bone: Techniques and Applications (Biomechanical Systems Technology: Muscular Skeletal Systems), World Scientific Pub. Co. Pte. Ltd., Singapore.
  6. Grimal, Q., Rus, G., Parnell, W.J. and Laugier, P. (2011), "A two-parameter model of the effective elastic tensor for cortical bone", J. Biomech., 44(8), 1621-1625.
  7. Guedes, J. and Kikuchi, N. (1990), "Preprocessing and postprocessing for materials based on the homogenization method with adaptive finite element methods", Comput. Methods Appl. Mech. Eng., 83(2), 143-198.
  8. Hollister, S.J., Brennan, J.M. and Kikuchi, N. (1994), "A homogenization sampling procedure for calculating trabecular bone effective stiffness and tissue level stress", J. Biomech., 27 (4), 433-444.
  9. Hollister, S.J., Fyhrie, D.P., Jepsen, K.J. and Goldstein, S.A. (1991) "Application of homogenization theory to the study of trabecular bone mechanics", J. Biomech., 24(9), 825-839.
  10. Homminga, J., Van-Rietbergen, B., Lochmuller, E.M., Weinans, H., Eckstein, F. and Huiskes, R. (2004), "The osteoporotic vertebral structure is well adapted to the loads of daily life, but not to infrequent "error" loads", Bone, 34(3), 510-516.
  11. Keyak, J.H., Meagher, J.M., Skinner, H.B. and Mote, Jr. C.D. (1990), "Automated three-dimensional finite element modelling of bone: A new method", J. Biomed. Eng., 12(5), 389-397.
  12. Kinney, J.H. and Ladd, A.J.C. (1998), "The relationship between three-dimensional connectivity and the elastic properties of trabecular bone", J. Bone Miner. Res., 13(5), 839-845.
  13. Kuhlemeyer, R.L. and Lysmer, J. (1973), "Finite element method accuracy for wave propagation problems", J. Soil Mech. Found. Div., Proc. Am Soc. Civil Eng., 99(5), 421-427.
  14. Lee, S.G., Gokhale, A.M. and Sreeranganathan, A. (2006), "Reconstruction and visualization of complex 3D pore morphologies in a high-pressure die-cast magnesium alloy", Mater. Sci. Eng.: A, 427(1), 92-98.
  15. Lewy, H., Friedrichs, K. and Courant, R. (1967), "On the partial difference equations of mathematical physics", IBM J. Res. Dev., 11(2), 215-234.
  16. Lin, C. and Cohen, M.H. (1982), "Quantitative methods for microgeometric modeling", J. Appl. Phys., 53(6), 4152-4165.
  17. Liu, X.S., Bevill, G., Keaveny, T.M., Sajda, P. and Guo, X.E. (2009), "Micromechanical analyses of vertebral trabecular bone based on individual trabeculae segmentation of plates and rods", J. Biomech., 42(3), 249-256.
  18. Liu, X.S., Sajda, P., Saha, P.K., Wehrli, F.W., Bevill, G., Keaveny, T.M. and Guo, X.E. (2008), "Complete volumetric decomposition of individual trabecular plates and rods and its morphological correlations with anisotropic elastic moduli in human trabecular bone", J. Bone Miner. Res., 23(2), 223-235.
  19. Lysmer, J. and Kuhlemeyer, R.L. (1969), "Finite dynamic model for infinite media", J. Eng. Mech. Div., Proc. Am. Soc. Civil Eng., 95(4), 859-877.
  20. Matsunaga, S., Naito, H., Tamatsu, Y., Takano, N., Abe, S. and Ide, Y. (2013), "Consideration of shear modulus in biomechanical analysis of peri-implant jaw bone: Accuracy verification using image-based multi-scale simulation", Dental Mater. J., 32(3), 425-432.
  21. Nakano, T., Kaibara, K., Tabata, Y., Nagata, N., Enomoto, S., Marukawa, E. and Umakoshi, Y. (2002), "Unique alignment and texture of biological apatite crystallites in typical calcified tissues analyzed by microbeam x-ray diffractometer system", Bone, 31(4), 479-487.
  22. Ohashi, T., Matsunaga, S., Nakahara, K., Abe, S., Ide, Y., Tamatsu, Y. and Takano, N. (2010), "Biomechanical role of peri-implant trabecular structures during vertical loading", Clin. Oral Investig., 14(5), 507-513.
  23. Parnell, W.J., Grimal, Q., Abrahams, I.D. and Laugier, P. (2006), "Modelling cortical bone using the method of asymptotic homogenization", J. Biomech., 39(1), S20.
  24. Pothuaud, L., Porion, P., Lespessailles, E., Benhamou, C.L. and Levitz, P. (2000), "A new method for three - dimensional skeleton graph analysis of porous media: application to trabecular bone microarchitecture", J. Microscopy, 199(2), 149-161.
  25. Reilly, D.T. and Burstein, A.H. (1975), "The elastic and ultimate properties of compact bone tissue", J. Biomech., 8(6), 393-405.
  26. Rho, J.Y., Ashman, R.B. and Turner, C.H. (1993), "Young's modulus of trabecular and cortical bone material: Ultrasonic and microtensile measurements", J. Biomech., 26(2), 111-119.
  27. Saha, P.K., Gomberg, B.R. and Wehrli, F.W. (2000), "Three-dimensional digital topological characterization of cancellous bone architecture", Int. J. Imaging Syst. Technol., 11(1), 81-90.<81::AID-IMA9>3.0.CO;2-1
  28. Shi, X., Wang, X. and Niebur, G.L. (2009), "Effects of loading orientation on the morphology of the predicted yielded regions in trabecular bone", Ann. Biomed. Eng., 37(2), 354-362.
  29. Stauber, M. and Muller, R. (2006), "Volumetric spatial decomposition of trabecular bone into rods and plates-A new method for local bone morphometry", Bone, 38(4), 475-84.
  30. Takano, N., Fukasawa, K. and Nishiyabu, K. (2010), "Structural strength prediction for porous titanium based on micro-stress concentration by micro-CT image-based multiscale simulation", Int. J. Mech. Sci., 52(2), 229-235.
  31. Takano, N., Zako, M., Kubo, F. and Kimura, K. (2003), "Microstructure-based stress analysis and evaluation for porous ceramics by homogenization method with digital image-based modeling", Int. J. Solid. Struct., 40(5), 1225-1242.
  32. Tawara, D., Adachi, T., Takano, N., Nakano, T., Umakoshi, Y., Kobayashi, A., Iwaki, H. and Takaoka, K. (2008), "High-resolution micro-mechanical analysis of cancelluos bone in vertebra considering bone quality", Jpn. J. Clin. Biomech., 29, 7-14. (in Japanese)
  33. Tawara, D., Takano, N., Adachi, T. and Nakano, T. (2010), "Mechanical evaluation of trabecular bone of human vertebra based on multi-scale stress analysis", J. Jpn. Soc. Bone Morphom., 20, S100-S107. (in Japanese)
  34. Van Buskirk, W.C. and Ashman, R.B. (1981), "The elastic moduli of bone", Tran. Am. Soc. Mech. Eng. (Appl. Mech. Div.), 45, 131-143.