Calcified Tissue International

, Volume 53, Supplement 1, pp S127–S133 | Cite as

Measurement and significance of three-dimensional architecture to the mechanical integrity of trabecular bone

  • Steven A. Goldstein
  • Robert Goulet
  • Doris McCubbrey
Session VI


The mechanical properties of trabecular bone have been shown to vary significantly with age, anatomic location, and metabolic condition. Efforts towards predicting its behavior have been extensive, and significant relationship between measures of density and mechanical integrity have been reported. Unfortunately, the significant heterogeneity in trabecular bone anisotropy contributes to significant unexplained variance in its strength and modulus when predicted using scalar measures of mass or density. As a result, numerous investigators have attempted to include measures of architecture in an effort to more rigorously investigate potential physiologic optimization strategies, as well as account for the increased fragility associated with advancing age. In our laboratories we have utilized a unique three-dimensional, microcomputed tomography system to measure trabecular plate thickness, trabecular plate separation, trabecular plate number, surface to volume ratio, bone volume fraction, anisotropy, and connectivity in isolated specimens of trabecular bone. The results of these studies demonstrate that in normal bone, more than 80% of the variance in its mechanical behavior can be explained by measures of density and orientation. The independent measures of connectivity and trabecular plate number were found to be significantly correlated with bone volume fraction, suggesting a potential strategy in the formation of trabecular bone. It might be hypothesized, however, that the relationship between bone volume fraction and connectivity may be substantially altered under conditions associated with aging, fragility, or metabolic bone disease. This hypothesis would be consistent with the histologic, evidence of reduced connectivity in osteopenic patients.

Key words

Trabecular bone Density Mechanical integrity 


  1. 1.
    Brand R, Claes L (1989) Review: the Law of bone remodeling by Julius Wolff. J Biomech 22(2):185–187Google Scholar
  2. 2.
    Carter DR, Orr TE, Fyhrie DP (1989) Relationships between loading history and femoral cancellous bone architecture. J Biomech 22(3):231–244Google Scholar
  3. 3.
    Cowin SC (1986) Wolffs law of trabecular architecture at remodeling equilibrium. J Biomed Eng 108:83–88Google Scholar
  4. 4.
    Hayes WC, Snyder B (1981) Toward a quantitative formulation of Wolffs law in trabecular bone. In: Cowin SC (eds) Mechanical properties of bone. ASME, pp 43–68Google Scholar
  5. 5.
    Koch JC (1917) The laws of bone architecture. Am J Anat 21:177–298Google Scholar
  6. 6.
    Lanyon, LE (1974) Experimental support for the trajectorial theory of bone structure. J Bone Jt Surg 56B(1):160–166Google Scholar
  7. 7.
    Raux P, Townsend PR, Miegel R, Rose RM, Radin EL (1975) Trabecular architecture of the human patella. J Biomech 8:1–7Google Scholar
  8. 8.
    Roux W (1895) Gesameltz Abhandlungen über der Entwicklungsmechanik der Organisman. Leipsiz, W. EngelmannGoogle Scholar
  9. 9.
    Goldstein SA (1987) The mechanical properties of trabecular bone: dependence on anatomical location and function. J Biomech 20:1055–1061Google Scholar
  10. 10.
    Kragstrup J, Melsen F, Mosekilde L (1983) Thickness of bone formed at remodelling sites in normal human iliac trabecular bone: variations with age and sex. Metab Bone Dis Rel Res 4:291–295Google Scholar
  11. 11.
    Lips P, Courpron P, Meunier PJ (1978) Mean wall thickness of trabecular bone packets in human iliac crest: changes with age. Calcif Tissue Res 26:13–17Google Scholar
  12. 12.
    McCubbrey DA, Goldstein SA, Cody DD, Goulet RW, Kuhn JL (1991) The regional density, architectural, and tissue properties of vertebral trabecular bone and their relation to whole bone failure properties. Adv Bioeng 20:575Google Scholar
  13. 13.
    Mosekilde L (1989) Sex differences in age-related loss of vertebral trabecular bone mass and structure: biomechanical consequences. Bone 10:425–432Google Scholar
  14. 14.
    Parfitt AM, Mathews CHE, Villaneuva AR, Kleerekoper M, Frame B, Rao DS (1983) Relationships between surface, volume, and thickness of iliac trabecular bone in aging and in osteoporosis. J Clin Invest 72:1396–1409Google Scholar
  15. 15.
    Parfitt AM (1984) Age-related structural changes in trabecular and cortical bone: cellular mechanisms and biomechanical consequences. Calcif Tissue Int 365:123–128Google Scholar
  16. 16.
    Snyder BD (1991) Anisotropic structure-property relations for trabecular bone. Ph.D. Thesis, University of Pennsylvania, Philadelphia, PA, 1991Google Scholar
  17. 17.
    Brown TD, Ferguson AB (1980) Mechanical property distributions in the cancellous bone of the human proximal femur. Acta Orthop Scand 51:429–437Google Scholar
  18. 18.
    Carter DR, Hayes WC (1977) The compressive behavior of bone as a two-phase porous structure. J Bone Joint Surg 59-A(7):954–962Google Scholar
  19. 19.
    Ciarelli MJ, Goldstein SA, Kuhn JL, Cody DD, Brown M (1991) The orthogonal mechanical properties and density of human trabecular bone from the major metaphyseal regions utilizing materials testing and computed tomography. J Orthop Res 9:674–682Google Scholar
  20. 20.
    Rice JC, Cowin S, Bowman JA (1988) On the dependence of elasticity and strength of cancellous bone on apparent density. J Biomech 21:155–168Google Scholar
  21. 21.
    Feldkamp LA, Goldstein SA, Parfitt AM, Jesion G, Kleerekoper M (1989) The direct examination of three-dimensional bone architecture in vitro by computed tomography. J Bone Miner Res 4:3–11Google Scholar
  22. 22.
    Goulet RW, Ciarelli MJ, Goldstein SA, Kuhn JL, Feldkamp LA, Kruger D, Viviano D, Champlain F, Matthews LS (1988) The effects of architecture and morphology on the mechanical properties of trabecular bone. Trans 34th Orthop Res Soc 13:73Google Scholar
  23. 23.
    Kuhn JL, Goldstein SA, Feldkamp LA, Goulet RW, Jesion G (1990) Evaluation of a microcomputed tomography system to study trabecular bone structure. J Orthop Res 8:833–842Google Scholar
  24. 24.
    Singh I (1978) The architecture of cancellous bone. J Anat 127:305–310Google Scholar
  25. 25.
    Whitehouse WJ (1974) The quantitative morphology of anisotropic trabecular bone. J Microsc 101(2):153–168Google Scholar
  26. 26.
    Merz WA, Schenk RK (1970) Quantitative structural analysis of human cancellous bone. Acta Anat 75:54–66Google Scholar
  27. 27.
    Odgaard A, Jensen EB, Gundersen HJG (1990) Estimation of structural anisotropy based on volume orientation. A new concept. J Microscopy 157:149–162Google Scholar
  28. 28.
    Pugh JW, Radin EL, Rose RM (1974) Quantitative studies of human subchondral cancellous bone. J Bone Joint Surg [Am] 56-A(2):313–321Google Scholar
  29. 29.
    Kuhn JL, Goulet RW, Goldstein SA, Feldkamp LA (1988) A study of variation of trabecular architectures in small volumes of bone using a microcomputed tomography system. Proc 12th American Soc of Biomechanics Meeting, Urbana-Champaign, Illinois, pp 16–17Google Scholar
  30. 30.
    Goulet RW, Goldstein SA, Ciarelli MJ, Kuhn JL, Brown MD, Feldkamp LA (in press) Relationship between the structural and orthogonal mechanical properties of trabecular bone. J BiomechGoogle Scholar
  31. 31.
    Serra J (1982) Image analysis and mathematical morphology. Academic Press, LondonGoogle Scholar
  32. 32.
    Kuhn JL, Goldstein SA, Choi K, London M, Feldkamp LA, Matthews LS (1989) A comparison of the trabecular and cortical tissue moduli from human iliac crests. J Orthop Res 7:95–107Google Scholar
  33. 33.
    Choi K, Khun JL, Ciarelli MJ, Goldstein SA (1990) The elastic moduli of human subchondral, trabecular, and cortical bone tissue and the size-dependency of cortical bone modulus. J Biomech 23:1103–1113Google Scholar
  34. 34.
    Choi K, Goldstein SA (1992) The fatigue properties of human trabecular bone tissue. J Biomech 25(12):1371–1381Google Scholar
  35. 35.
    McCubbrey DA, Yian EH, Goulet RW, Shih MS, Parfitt AM, Goldstein SA (1993) The effects of calcitonin on trabecular bone properties in the ovariectomized beagle. Transactions of the 1993 Orthopaedic Research Society Meeting, February 1993Google Scholar
  36. 36.
    Faugere MC, Friedler RM, Fanti P, Malluche HH (1990) Bone changes occurring early after cessation of ovarian in beagle dogs: a histomorphometric study employing sequential biopsies. J Bone Miner Res 5:263–272Google Scholar
  37. 37.
    Martin RB, Butcher RL, Sherwood LL, Buckendahl P, Boyd RD, Farris D, Sharkey N, Dannicci G (1987) Effects of ovariectomy in beagle dogs. Bone 8:23–31Google Scholar
  38. 38.
    Malluche HH, Faugere MC, Rush M, Friedler R (1986) Osteoblastic insufficiency is responsible for maintenance of osteopenia after loss of ovarian function in experimental beagle dogs. Endocrinology 119:2649–2654Google Scholar
  39. 39.
    Vesterby A, Gundersen HJG, Melsen F (1989) Star volume of marrow space and trabeculae of the first lumbar vertebra: sampling efficiency and biological variation. Bone 10:7–13Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1993

Authors and Affiliations

  • Steven A. Goldstein
    • 1
  • Robert Goulet
    • 1
  • Doris McCubbrey
    • 1
  1. 1.Orthopaedic Research Laboratories, Section of Orthopaedic SurgeryUniversity of MichiganAnn ArborUSA

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