Examination of continuum and micro-structural properties of human vertebral cancellous bone using combined cellular solid models

Two- and three-dimensional structural models of the vertebral body have been used to estimate the mechanical importance of parameters that are difficult to quantify experimentally such as lattice disorder, trabecular thickness, trabecular spacing, connectivity, and fabric. Many of the models that investigate structure–function relationships of the vertebral body focus only on the trabecular architecture and neglect solid–fluid interactions. We developed a cellular solid model composed of two idealized unit cell geometries to investigate the continuum and micro-structural properties of human vertebral cancellous bone in a mathematically tractable model. Using existing histomorphological data we developed structure–function relationships for the mechanical properties of the solid phase, estimated the micro-structural strains, and predicted the fluid flow characteristics. We found that the micro-structural strains may be 1.7 to 2.2 times higher than the continuum level strains between the ages of 40 and 80. In addition, the predicted permeability agrees well with the experimental data.