A stereological method for calculating internal surface areas in structures which have become anisotropic as the result of linear expansions or contractions

SUMMARY It is postulated that there may be classes of microstructures, having anisotropic internal features, which are related to internally isotropic structures by a coordinate transformation. Such structures are known to occur, for instance, in metallography when the bulk material has been subjected to deformation and there are many biological analogies. The simplest case of coordinate transformation is investigated theoretically in this paper; that of a linear transformation in one dimension. Formulae have been found for the numerical constant which allows the density of the internal surface which separates two components of the material to be calculated from the border profile density on a plane section through the material. Measurements on trabecular bone have suggested that it may be a structure of this type, and, on this assumption, the errors due to incorrectly assuming isotropy, when calculating the area of the surface which separates the bone from the marrow, are discussed.