DIRECT CALCULATION OF THE SURFACE-TO-VOLUME RATIO FOR HUMAN CANCELLOUS BONE

There are many diseases which cause detrimental changes in the trabecu lar structure of cancellous bone, leading to mechanical failure of the tissue. One approach to understanding the mechanisms of these disease s is to create idealized models that recreate the morphology of the ti ssue. This paper presents a partial development of such a model. Furth er histological methods must be developed before a complete definition of morphologically valid models is possible. In a histological sectio n of cancellous bone, the orientation and length of the trabecular sur faces determine how a line drawn across the bone section will intersec t the bone-marrow interface. The distribution of the average length be tween intersections for a set of parallel lines is defined as the mean intercept length distribution. In this paper, the average surface mor phology and volume of the average structure of cancellous bone is dete rmined from an examination of the mean intercept length. The average s tructure 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=0.017kappa(BV/TV)-2.05 mm3, R2= 0.93, with kappa a model-dependent constant. For the same specimens, t he structural element surface (SE.S) showed the relationship, SE.S=0.1 44kappa(BV/TV)-1.35, R2=0.92. As a result of the inverse square depend ence of structural element volume on bone volume fraction, it is predi cted that cancellous bone strength is inversely proportional to struct ural element volume.