Fractal dimension and mechanical properties of human cortical bone

Fractal dimension (FD) can be used to characterize microstructure of porous media, particularly bone tissue. The porous microstructure of cortical bone is observable in micro-CT (μCT) images. Estimations of fractal dimensions of μCT images of coupons of human cortical bone are obtained. The same samples were tested on a tensile test machine and Young's modulus (YM) and Failure stress were obtained. When both types of measures were compared, a clear correlation was found (R=-81%, P<0.01). Young's modulus of each sample and the FD of its μCT images are correlated. From the assumption that cortical bone is approximately a fractal set, a non-linear constitutive relation involving FD is obtained for YM. Experimental results show good agreement with this constitutive relation. Additional parameters in the non-linear relation between YM and FD have been estimated from experimental results and related to physical parameters.