ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

the intrinsic problems of this very material, a discontinuity will persist in the repaired
tissue. It will so prohibit the complete restoration of the bone tissue and, particularly, of
its vascularization.
A solution developed these last years consists in manufacturing a hybrid biomaterial,
i.e. a ceramic pre-colonized by cells, for example osteoblasts for bone tissue restoration
or endothelial cells for vascularization restoration 2-3 . It aims to facilitate the in situ cells
to assimilate the volume once grafted. The future implant is so seeded then put in a
culture medium. Static conditions (the scaffold dips in a flask) are sufficient for small
volumes. For larger scaffolds, the initial problem remains: feeding the cells even far
from the interface and evacuating their waste, difficult indeed impossible for large
bulks. In such a case dynamic conditions are necessary to allow the medium to reach all
the cells on pain of cell death. Devices called bioreactors are then used usually more or
less elaborate and complicated pump systems to perfuse the scaffold 4 .
Of course a bioceramic must be macroporous with interconnected pores to allow the
cells to settle and to develop and the medium to circulate through the entire scaffold 5 .
The importance of the pressure and of the velocity of the medium is well known for the
survival and the proliferation of the cells. But the problem consists thenceforth in
determining the input flow leading to the optimal pressure and velocity in any pore.
Indeed the size of usual such internal structures does not allow to experimentally
measure these parameters. The input condition so usually depends on the expertise of
the biologists and can change according to the geometry and to the internal structure of
the scaffold. Developing a numerical method to modelize then to calculate these
parameters according to the pump output would be time saver and an interesting way to
lead to the optimal growing conditions.
The first step of our works, exposed in this paper, so aims to identify through numerical
modeling the permeability of a macroporous bioceramic used as a bone substitute.
Indeed the permeability allows reaching the velocity and the pressure of the flow
through the Darcy's law, a phenomenological derived constitutive equation that
describes the flow of a fluid through a porous medium. This parameter is then
fundamental and our first step for the numerical determination of the velocity and the
pressure in the heart of a bioceramic. The macroporosity of this bioceramic is indeed
controlled and open; randomly arranged spherical macropores (diameter 600 µm) are
interconnected (diameter 100 µm) and it allows the medium to circulate through the
whole bulk 6 .
Due to the size of the macropores of the ceramic and of their interconnections, the flow
across them can be considered near the micro-fluidic domain and the influence of
gravity can be neglected. The very low mass flow rate generally chosen by the
biologists leads to a steady laminar regime for the fluid flow. So, after having
remembered the basis of the theoretical determination of the permeability, our work has
consisted in identifying some behavior laws fitting to this type of flow regime for a
macroscopic scale and being able to lead to this parameter. The limits of these empirical
or analytical models have then led to look for a numerical model to directly solve fluid
mechanics equations. The results in term of permeability or dimensionless permeability
are compared for some systems able to describe the real macroporous bioceramic and its
internal structure while a numerical method to apprehend whole complex bioceramic
bulks has been searched. The chosen method, model, system and calculation, have
finally been validated.
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