In Silico Biology of Bone Regeneration Inside Calcium Phosphate Scaffolds - Tissue Engineering: Computer Modeling, Biofabrication and Cell Behavior - page 38

Fig. 2 Amount of bone
formation at day 90 as a
function of the calcium
release rate ( σ ) and initial
MSC concentration ( c m 0 )
according to the mathematical
model
After the development and validation of the model, the model needs to be further
analyzed and can be used for optimization. The analysis phase allows determining
which factors are the most important ones and how they interact. This is another
major advantage of modeling. Since biological systems are so complex, it is often
difficult to intuitively predict what will happen if a specific factor is changed. To
determine the most influential factors of the mathematical model, Carlier et al. [ 11 ]
performed a sensitivity analysis by “Design of Experiments” (DOE). DOE is a sta-
tistical tool that enables the determination of an efficient design for (in this case)
a multi-parameter sensitivity analysis. Carlier et al. [ 11 ] used the JMP statistical
software (8.0.1. SAS Institute Inc.) to generate the array of combinations of differ-
ent parameter values within a pre-defined parameter space. The sensitivity analysis
showed that the bone formation rate P bb , the initial MSC density c m 0 and the ini-
tial osteoblast density c b 0 are the most important factors influencing the amount of
bone formation at day 21 and 42 [ 11 ]. The model outcome also largely depends
on the initial conditions, which therefore should be realistically defined. The sen-
sitivity analysis indicated a significant interaction between the calcium release and
the initial MSC seeding density which was subsequently further investigated (see
Fig. 2 ). The model indicates that a low initial MSC density requires a low calcium
release rate, while a high initial MSC density requires a high calcium release rate
in order to maximize the amount of bone formation. The amount of bone formation
for low initial MSC concentrations is also very sensitive to calcium, whereas high
initial MSC concentrations produce similar amounts of bone for a range of calcium
release. For tissue engineering strategies it is interesting to start with a low initial
cell density but since the margin is very small, the optimization is critical for these
types of constructs. The high MSC concentrations entail a larger window of allow-
able calcium release rates which allows for more optimization and potentially higher
benefits. The in vivo bone formation capacity of different CaP scaffolds seeded with
a fixed concentration of hPDCs was studied by Roberts et al. [ 36 ]. They found that
the calcium release rate is a strong determinant in discriminating bone-forming scaf-
folds from scaffolds that did not lead to any bone formation thereby confirming our
initial hypothesis. This integrative research shows that mathematical models can be