Compact and cancellous bone behave as a “bimaterial beam model” of constant strength

Abstract

A mechanical model of bone should describe stress and strain distributions according to minimum/maximum laws. At the macrolevel the shape of the bone enables the support of significant loads if these are applied in physiological directions. With this concept in mind we have examined the geometric distributions of compact and cancellous bone and compared these to variations of V in the shear diagram and M in the bending moment diagram respectively. Two types of analytical methods have been used: (i) basic mechanical models of cylindrical and fusiform tube shapes with different thicknesses of tube plates, all compared with bone and presented as FEM models ; (ii) FEM models of human long bones obtained from CT data. Preprocessing was carried out using CATIA V5R14, and ABAQUS/Standard was used for subsequent analysis. In this analysis FEM simulation of different bending tests was performed in all samples. It was observed that there were: (a) variations of V in the shear diagram and M in the bending moment diagram according to the shape, (b) variations of the cortical thickness of different cross sections of bone shafts according to the polar moment of inertia and (c) variations of the CT densities of bone tissue and Young's modulus of elasticity distribution according to previously published data. The results from these models indicate that the local compact bone volume mainly correlates with the bending moment stresses and cancellous bone volume correlates with the shear stresses. Bone avoids higher local stresses by distributing the internal forces and bone volume according to a minimum/maximum law which continuously optimises the bone shape to one with constant strength.