| [ Summary ] |
Microarchitecture of trabecular bone has been examined with a particular emphasis of surface curvatures in two-phase (trabecula and intertrabecula space, i.e., marrow space) structures. Three trabecular bone samples, quantified to be "plate-like", "rod-like" and mixture of these two structural elements by the Structure Model Index (SMI), were subjected to the analysis based on (differential) geometry. A new method to measure surface curvatures is proposed. The Gaussian curvatures for the three bone structures were found to be all negative, clearly demonstrating that their surfaces are hyperbolic irrespective of the SMI values. This finding is in contrast with the existing common concept that bone microarchitectures consist of either plate or rod elements (both be longing to the parabolic surface). In addition, the Euler-poincare characteristics and the genus, both characterizing the topological features of the bone connectivity, were estimated from the integral Gaussian curvature. The three bone microarchitectures were found to be topologically analogous to spheres with one to three handles. The number of handles, representing complexity of the micro structure, seems to be consistent with visual impression of the bone specimens. |