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Abstract
Cortical bone has two systems of interconnected channels. The largest of these is
the vascular porosity consisting of Haversian and Volkmann's canals, with a diameter
of about 50 microm, which contains a.o. blood vessels and nerves. The smaller is the
system consisting of the canaliculi and lacunae: the canaliculi are at the submicron
level and house the protrusions of the osteocytes. When bone is differentially loaded,
fluids within the solid matrix sustain a pressure gradient that drives a flow. It
is generally assumed that the flow of extracellular fluid around osteocytes plays
an important role not only in the nutrition of these cells, but also in the bone's
mechanosensory system. The interaction between the deformation of the bone matrix
and the flow of fluid can be modelled using Biot's theory of poroelasticity. However,
due to the inhomogeneity of the bone matrix and the scale of the porosities, it is
not possible to experimentally determine all the parameters that are needed for numerical
implementation. The purpose of this paper is to derive these parameters using composite
modelling and experimental data from literature. A full set of constants is estimated
for a linear isotropic description of cortical bone as a two-level porous medium.
Bone, however, has a wide variety of mechanical and structural properties; with the
theoretical relationships described in this note, poroelastic parameters can be derived
for other bone types using their specific experimental data sets.