In Vivo, In Vitro, In Silico: Computational Tools for Product and Process Design in Tissue Engineering - Computational Modeling in Tissue Engineering - page 9

unknown that requires thorough experimental investigation. From the obtained
experimental results mechanisms of actions can be proposed and subsequently
mathematical models can be used to translate these mechanisms of action into a
coherent set of mathematical equations. These equations form a quantitative
spatio-temporal framework of interrelated biological variables and sub-processes,
providing a dynamic and comprehensive overview of the entire repair process. As
such, the mathematical models can help in interpreting the in vivo data (by
establishing causal relations) on the one hand and generating new hypotheses on in
vivo outcome (by running in silico experiments) on the other hand, in this way
adding to the design and optimization of TE products and processes.
A myriad of models has been proposed in the literature describing various
pathologies and in vivo regenerative processes. Watton et al. [ 49 ] have developed
a fluid-solid-growth model to simulate the evolution of abdominal aortic aneu-
rysms. The model uses a realistic constitutive model of the arterial wall accounting
for a wide number of lower scale structures and processes. With the help of this
model they were able to predict e.g. the development of tortuosity that accom-
panies abdominal aortic aneurysm enlargement. Besides providing a basis for
further investigation and elucidation of the aetiology of aneurysm formation, the
computational framework can also be applied to aid the design and optimisation of
tissue engineered vascular constructs. In the field of bone regeneration Geris et al.
[ 50 ] have reviewed the existing models of fracture healing, dividing these models
into bioregulatory (fracture healing guided by biological stimuli), mechanoregu-
latory (fracture healing guided by mechanical stimuli) and mechanobioregulatory
models (fracture healing guided by mechanical and biological stimuli). Nagel and
Kelly [ 51 ] adapted a well-known mechanoregulatory model to explicitly account
for the influence of oxygen tension on tissue differentiation. They furthermore
discuss the effects of incorporating the tissue architecture during skeletal regen-
eration as well as the variability of the process. Reina-Romo et al. [ 52 ] discuss the
importance of angiogenesis on both bone regeneration and TE. They describe the
role of the vascular network in these processes as well as the most recent in silico
models simulating the vascular network within bone constructs. They analyse
discrete as well as continuum approaches from a computational perspective.
As mentioned above, simulation of the behaviour of a TE construct after
implantation is another crucial aspect in the optimisation of TE products and
processes. Lemon et al. [ 53 ] have developed a mathematical model of the
regeneration of a tissue-engineered trachea seeded with cells in situ, in order to
study the biological processes (e.g. stenosis) taking place after implantation for
various designs of the TE construct (different cell seeding strategies). They pro-
vide an in depth discussion on the obstacles that are encountered when trying to
formulate a faithful model of (any kind of) biological product or process.
Furthermore they investigate how a simplified mathematical model that omits
much detail of the biology can be of use for studying regeneration of a TE
construct, using their model of a tissue-engineered trachea as an example.