Statistical model of the habit and arrangement of mineral crystals in the collagen of bone

Abstract

Randomly colored space tesselations are considered as models for the mineral/organic structure of bone. First, it is shown that the structure function for such models is always proportional to the average form factor of the individual tiles and hence independent of the mineral density in the sample. Then the structure function is calculated for three such models: for model I, based on a hexagonal, and model 2, on a Poisson-Voronoi tesselation of the plane and for model 3, based on a random tesselation of the line. These results are compared to experimental structure functions measured by small-angle scattering and excellent agreement is obtained between model 2 and the bone from mice and rats, as well as between model 3 and calcified turkey leg tendon. Divergent conclusions following recent experiments by small-angle x-ray scattering and by electron microscopy are discussed in the light of these structural models and an explanation is proposed which might remove the discrepancy.