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

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.