Optimal cut of trabecular network

Abstract 

It has been shown recently that failure of mechanically tested trabecular bone samples can be localized within a part of the volume of the samples. Bone volume fraction BV/TV of failure regions was found to be a better determinant of the mechanical competence of the specimens and was smaller than BV/TV of the whole samples. These results suggest that localization of a failure within a part of an inhomogeneous trabecular network can be related to the presence of a surface of minimal cut—a surface separating the analyzed trabecular sample into two disjoint parts in such a way, that the separation requires removal of minimal possible amount of bone material. Thus, to properly address the problem of mechanical competence of a trabecular bone sample, one must be able to detect and describe the surface of minimal cut. In this paper an algorithm localizing surfaces of minimal cut within 3D trabecular structures is introduced.

Keywords: Graph theory, Graph partitioning, Fiedler vector, Microtomography