In Silico Biology of Bone Regeneration Inside Calcium Phosphate Scaffolds - Tissue Engineering: Computer Modeling, Biofabrication and Cell Behavior - page 34

of ion concentration need to be determined and optimized for a specific in vitro and
in vivo response.
3 Mathematical Models of Bone Regeneration Inside (CaP)
Scaffolds
3.1 From Models...
Improvements in computer capacity now enable an increased model realism
and complexity (e.g. 3D calculations, complex geometries, multi-scale, multi-
physics, ... )[ 45 ]. As a consequence of this technological revolution, there has been
an enormous increase in the use of mathematical models in biology and medicine.
These mathematical models can propose and test possible biological mechanisms,
contributing to the unraveling of the complex nature of biological systems. More-
over, they can be used to design and test possible experimental strategies in silico
before they are tested in vitro or in vivo . Finally, all this knowledge can be used to
develop clinically relevant cell carriers.
Currently, many computational models of bone formation and regeneration in
general (reviewed in Geris et al. [ 16 - 18 ]), or even in (CaP) scaffolds specifically
(reviewed in Sengers et al. [ 39 ]) exist. Bohner et al. [ 6 ] propose a theoretical ap-
proach to determine the effect of geometrical factors on the resorption rate of CaP
scaffolds. The theoretical model was based on five assumptions: (i) the pores are
spherical, (ii) the pores follow a face-centered cubic packing, (iii) the resorption is
surface-controlled, (iv) the resorption requires the presence of blood vessels (50 µm
in diameter) and (v) the resorption time is proportional to the net amount of mate-
rial [ 6 ]. Based on these assumptions the model calculations show that the resorption
time of a macroporous block depends on the pore radius which is dependent on the
size of the bone substitute and the interpore distance [ 6 ]. The model was also used
to optimize the pore size of CaP scaffolds and validated with experimental data. The
theoretical model looks, however, exclusively at geometrical scaffold properties and
does not include biological variables such as cells or matrix densities. Byrne et
al. [ 8 ] developed a 3D mechanoregulatory model of bone regeneration in a regu-
lar scaffold to investigate the effect of porosity, Young's modulus and dissolution
rate on bone regeneration in different loading conditions. They model the scaffold
degradation in a linear, load-independent fashion, i.e. the porosity will be increased
bya0%,0.5%,1%periterationforlow,intermediateandhighdissolutionrates
respectively [ 8 ]. Consequently, the size of all scaffold elements decreases uniformly
resulting in an overall volumetric reduction while the scaffold geometry remains
unaltered [ 8 ]. Their calculations show that as scaffold degradation progresses, the
regenerating tissue must take over the mechanical function of the bone-scaffold sys-
tem which would otherwise collapse due to a lack of mechanical strength [ 8 ]. More-
over, all three variables (i.e. porosity, Young's modulus and dissolution rate) appear
to influence the amount of bone formation in a non-intuitive way, demonstrating