In Silico Biology of Bone Regeneration Inside Calcium Phosphate Scaffolds - Tissue Engineering: Computer Modeling, Biofabrication and Cell Behavior - page 42

for phosphorylation events to hours for mRNA transcription to weeks for tissue for-
mation and remodeling processes [ 26 ]. The spatial scales vary from nanometers at
the molecular level to millimeters at the tissue level and meters at the level of the
organism [ 26 , 30 ]. As such, one can conclude that the bone regeneration process
is a multiscale problem and should be studied and modeled accordingly. Some at-
tempts have already been made like Sanz-Herrera et al. [ 38 ] who use a multiscale
modeling approach to determine the role of the scaffold microarchitecture in bone
tissue regeneration. Besides some localized activities, coordinated efforts should
also focus on the integration of models at different biological scales [ 26 ]. Liu et al.
[ 26 ] propose for example an object-oriented module-based computational integra-
tion strategy to link currently available models of different methodologies (algebraic
equations, PDEs, AB). In this way the computational infrastructure effectively inte-
grates multiple modules by coordinating their connectivity and data exchange. Not
only does such a platform allow the straightforward combination of existing math-
ematical models, it is also intrinsically a multiscale modeling environment thereby
approaching the true multiscale nature of biological processes.
As already pinpointed in the previous section, quantitative data are crucial for
mathematical models to reach their true potential. Thus in vitro or in vivo experi-
ments should be designed so that they enable quantification. The highly controllable
and quantifiable environment is a major advantage of in vitro set-ups [ 18 ]. However,
the conclusions should be carefully translated to the actual in vivo environment since
the cells and tissues are isolated from their natural environment. The use of in vivo
models has the advantage of resembling the reality but quantification will be more
challenging. Moreover, as mathematical models predict the dynamics at different
scales (e.g. molecular, cellular and tissue) as a function of time and space, there is
a need for temporal and spatial experimental data. A possible strategy is the use
of imaging techniques (e.g. micro-computed tomography) that allow non-invasively
monitoring and quantification of the in vivo dynamics.
5Conclusion
This chapter discussed the biology of bone regeneration in CaP scaffolds and the
related modeling efforts. A number of advantages of mathematical modeling were
indicated and illustrated by examples of the bone tissue engineering field. It is clear
that only a true integrative approach, that combines mathematical modeling with
experimental research will help to further elucidate the biological process of bone
regeneration inside CaP scaffolds. The integrative strategy is necessary during both
the development of the model (determination of parameter values) and the model
validation phase (comparison of the model predictions to experimental findings).
Building this bridge between different disciplines requires a lot of effort but it is the
only way to truly obtain predictive models that can be used to advance the research
in the bone tissue engineering field.