Direct calculation of the surface-to-volume ratio for human cancellous bone

Fyhrie, D. P.<sup>1</sup>; Fazzalari, N. L.<sup>1,3</sup>; Goulet, R.<sup>2</sup>; Goldstein, S. A.<sup>2</sup>

Affiliations

¹Breech Research Laboratory, Bone and Joint Center Henry Ford Hospital, Detroit, MI 48202, U.S.A.

²The Orthopaedic Research Laboratories Orthopaedic Surgery, University of Michigan, Ann Arbor, Michigan, USA

³permanent address: Institute of Medical and Veterinary Science, Adelaide, Australia

Abstract

There are many diseases which cause detrimental changes in the trabecular structure of cancellous bone, leading to mechanical failure of the tissue. One approach to understanding the mechanisms of these diseases is to create idealized models that recreate the morphology of the tissue. This paper presents a partial development of such a model. Further histological methods must be developed before a complete definition of morphologically valid models is possible.

In a histological section of cancellous bone, the orientation and length of the trabecular surfaces determine how a line drawn across the bone section will intersect the bone-marrow interface. The distribution of the average length between intersections for a set of parallel lines is defined as the mean intercept length distribution. In this paper, the average surface morphology and volume of the average structure of cancellous bone is determined from an examination of the mean intercept length. The average structure of cancellous bone contains a repeated structural element (SE). As a result, the basic bone structure is analogous to a brick wall made from many similar bricks. For a group of 107 specimens, a strong relationship between structural element volume (SE.V) and bone volume fraction (BV/TV) is demonstrated, SE.V=0.017κ(BV/TV)^-2.05 mm³, R²=0.93, with κ a model-dependent constant. For the same specimens, the structural element surface (SE.S) showed the relationship, SE.S=0.144κ(BV/TV)^-1.35, R²=0.92. As a result of the inverse square dependence of structural element volume on bone volume fraction, it is predicted that cancellous bone strength is inversely proportional to structural element volume.

Links

DOI: 10.1016/0021-9290(93)90057-L

PubMed: 8349720

WoS: A1993LL52700005

History

Received: 1991-02-12

Accepted: 1992-12-8

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Cited By (11)

Year	Entry
1995	Majumdar S, Newitt D, Jergas M, Gies A, Chiu E, Osman D, Keltner J, Keyak J, Genant H. Evaluation of technical factors affecting the quantification of trabecular bone structure using magnetic resonance imaging. Bone. October 1995;17(4):417-430.
1997	Odgaard A. Three-dimensional methods for quantification of cancellous bone architecture. Bone. 1997;20(4):315-328.
1997	Beck JD, Canfield BL, Haddock SM, Chen TJH, Kothari M, Keaveny TM. Three-dimensional imaging of trabecular bone using the computer numerically controlled milling technique. Bone. 1997;21(3):281-287.
2011	Tassani S, Particelli F, Perilli E, Traina F, Baruffaldi F, Viceconti M. Dependence of trabecular structure on bone quantity: a comparison between osteoarthritic and non-pathological bone. Clin Biomech (Bristol, Avon). July 2011;26:632-639.
1998	Hou FJ, Lang SM, Hoshaw SJ, Reimann DA, Fyhrie DP. Human vertebral body apparent and hard tissue stiffness. J Biomech. November 1998;31(11):1009-1015.
1999	Jacobs CR, Davis BR, Rieger CJ, Francis JJ, Saad M, Fyhrie DP. The impact of boundary conditions and mesh size on the accuracy of cancellous bone tissue modulus determination using large-scale finite-element modeling. J Biomech. November 1999;32(11):1159-1164.
2009	Coelho PG, Fernandes PR, Rodrigues HC, Cardoso JB, Guedes JM. Numerical modeling of bone tissue adaptation: a hierarchical approach for bone apparent density and trabecular structure. J Biomech. May 11, 2009;42(7):830-837.
2011	Coelho PG, Fernandes PR, Rodrigues HC. Multiscale modeling of bone tissue with surface and permeability control. J Biomech. January 11, 2011;44(2):321-329.
1999	Yang G. Averaging and Bounding of Anisotropic Elastic Constants [PhD thesis]. New York, NY: The City University of New York; 1999.
2021	Shaffer SK. High-Speed Exercise and Fetlock Kinematics Affect the Development of Stress-Reactions in Racehorse Proximal Sesamoid Bones [PhD thesis]. Davis, University of California; 2021.
2001	Zhang N. Investigation of Bone Mechanical Properties At the Microscopic Level Using Ultrasonic Methods and Numerical Simulation [PhD thesis]. Detroit, MI: Wayne State University; 2001.