In Silico Biology of Bone Regeneration Inside Calcium Phosphate Scaffolds - Tissue Engineering: Computer Modeling, Biofabrication and Cell Behavior - page 37

ough understanding of the biological process under study. The modeler will need to
decide which variables are most important to answer the research question at hand
and how the underlying biological processes will be represented. Often this is done
in close collaboration with experimental biologists who might have a different view
and strategy of tackling problems. These very fundamental discussions and ques-
tions often lead to new insights and research tracks and are therefore a noteworthy
advantage of mathematical modeling.
Mathematical models can also be used to compute information that would be im-
possible to obtain experimentally. For example, Milan et al. [ 31 ] use a finite element
analysis to calculate the shear strain, fluid flow and pore pressures inside a porous
polymeric scaffold. Also Byrne et al. [ 8 ] use a finite element analysis to compute
the strain and fluid flow which are then used as input for the mechanoregulatory
model of tissue differentiation. It is clear that these biophysical stimuli play a key
role in the bone regeneration process. Besides the mechanoregulatory variables, also
bioregulatory variables are difficult to measure in an in vitro or in vivo setting. Car-
lier et al. [ 11 ] calculate the amount of calcium that is released by the CaP scaffold
and taken up by the osteogenic cells. Although this model is only one-dimensional,
an extension with spatial dimensions would allow the determination of the calcium
distribution inside the scaffold and developing tissue. This is important since cal-
cium influences many cellular processes as was shown in the previous section.
The experimental difficulties mentioned above entail however problems for
model validation. The results of a model have indeed no meaning if they are not cor-
roborated by real in vitro or in vivo data. This problem is often solved by measuring
related quantities and seeing how they correspond to the model predictions. Byrne
et al. [ 8 ] suggest for example to implant a scaffold into a bone defect in an animal
model and making histological measurements of tissue phenotype at several time
points which could then be compared to the simulation results. Another technique
is to use the model framework in a different application and determining whether
the predictions also fit in this new setting. The model of Carlier et al. [ 11 ] was vali-
dated by comparison with experimental data. Firstly, it was found that the model of
Carlier et al. [ 11 ] is able to reproduce the sequential events observed experimentally
during intramembranous healing: (1) proliferation, (2) differentiation, (3) collagen
production and (4) mineralization [ 29 , 41 ]. Secondly, the model results were com-
pared to the experimentally determined amount of bone formation by Hartman et al.
[ 21 ]. It was found that the results of the simulation and the experiment correspond
qualitatively. Thirdly, the modeling platform successfully predicted the absence of
bone in the impaired healing situations of scaffold decalcification and insufficient
cell seeding. However, the results of the model should be interpreted in a qualita-
tive way due to some simplifications and parameter value estimations. The current
tool would have much more potential if it could be made more quantitative. A major
problem in that respect is the lack of extensive characterization and quantification of
the scaffold properties. As such it is difficult to match the experimental conditions
found in literature with the modeled ones. Currently, specific in vivo and in vitro
testing procedures are being set up to determine the calcium release rate and relate
it to the in vivo bone forming capacity of different CaP scaffolds.