Human cortical bone: the SiNuPrOs model. Part II – a multi-scale study of permeability

Cortical bone is more and more considered as a porous medium and this induces the necessity of the determination of the physical properties associated with such a concept: the porosity and the permeability. If porosity does not present a major problem, at least for the order of magnitude, there is a difficulty for the permeability. According to experimental sources, values vary between 10− 13 and 10− 23 m2: it seems obvious that the same entities have not been measured. This article proposes a new vision of the permeability based on a concept of multi-scale medium corresponding to the scales already introduced in the SiNuPrOs model which has been developed for cortical bone. According to this model, several architectural levels are proposed and a mathematical development based on the homogenisation theory, which can be applied to each of these levels, allows a numerical computation of the permeability tensor coefficients. A comparative analysis of our simulations and some experimental results (already published) shows a good accordance with the literature.