Multiscale Approach to Understand the Multiphysics Phenomena in Bone Adaptation - Multiscale Computer Modeling in Biomechanics and Biomedical Engineering - page 45

Fig. 5 Representation of the macroscopic medium X (reference length L) and the periodic
representative cell Y (reference scale ' ). In the representative periodic cell, the fluid and solid
domains Y f (grey) and Y s (white) and the solid-fluid interface oY fs (dashed boundary) are shown
(reproduced with permission from [ 77 ])
determination of scaling laws, the consequences at the macroscale of these
microscopic phenomena are obtained.
Our strategy consists of discussing, at both the macroscale and the microscale,
the importance of the multiphysical phenomena featuring in bone behaviour using
physiologically-based simulations. That is why, in the first section, the ingredients
of our model are introduced. Then, some numerical examples are presented to
illustrate the interest of our multiscale approach. Through these simulations, we
are able to distinguish the phenomena that are purely microscopic from those
which can be macroscopically observed. Finally, from these multiscale consider-
ations, we propose some avenues which it is worth exploring when aiming at
in silico representing the bone remodelling process.
3 Multiphysics Model of the Bone Behaviour
The first step in our investigation consists in giving an accurate description of the
phenomena. The solid, the fluid and the fluid-solid interface are treated separately.
The representative periodic cell is built from anatomical considerations. Cortical
bone is seen as a fully saturated porous medium X : The relevant porosity level X f
for bone fluid electro-chemical phenomena corresponds to the lacuno-canalicular
porosity [ 84 ] whereas the origin of piezo-electricity is located in the collagen-
apatite matrix X s : Thus the representative elementary volume Y corresponds to a
periodic portion of the lacuno-canalicular network as shown in Fig. 5 . In this
representative periodic cell, the fluid and solid domains are noted Y f (grey) and Y s
(white) respectively and the solid-fluid interface oY fs : In cortical bone, the cana-
licular pores are occupied by a dendrite of the osteocyte cells (seen here as a part
of the solid phase) giving at the fluid domain an annular geometry. Note that we
neglect the influence of the larger porosity level of cortical bone corresponding
to vasculature. This assumption is grounded on the hierarchical multi-porous