Computational Models of Vascularization and Therapy in Tumor Growth - Mechanical and Chemical Signaling in Angiogenesis - page 229

parameters. Note that only a part of the parameters were found in the literature, the
others were fixed arbitrarily. A schematic view of the model is shown Fig. 3 .
Another example we would like to mention is the series of paper published by
Agur and coworkers. The author proposed a complex model to describe the pro-
cess of angiogenesis [ 39 ]. In this model, a particular attention is given to the
modeling hypothesis based on experimental evidences provided by Suri and
Maisonpierre, in particular, regarding the role of angiopoietin 1 and 2 [ 40 , 41 ]. The
authors have performed a validation study in comparing model predictions to
observations in animal experiments [ 42 ]. Another validation study was performed
in clinical data for mesenchymal patients [ 43 ].
The concept of multiscale modeling is indeed very appealing as it promises a
framework to integrate models develop at different scales. However, the main
problem relies in the excessive number of parameters they integrate for which it is
not possible to perform one unique experiment. As an example, one cannot expect to
measure molecular reaction rates and tissue dynamics in the same experimental set-
up. So, the only possibility to cope with this problem is to couple pieces of models,
carefully validated, together a modular structure. However, this modular framework
does not go without important methodological problems and limitations that must be
addressed. For instance, how to correctly balance a priori information (coming from
literature for instance) and the data-driven knowledge? How to efficiently include
or search for a priori information? This may require the development of sharing and
re-use resources among the community. How to assess the validation of such piece-
make models? And how to correctly 'jump' from one scale to another?
5 Specific Models for Intracellular and Intercellular
Aspects of Angiogenesis
a. Computational model of the dynamic of VEGFR2 signaling pathway
Another important aspects for the development of relevant multiscale model of
angiogenesis is the integration of intracellular mechanisms. The aim of this par-
agraph is to provide an example on a model targeting this level of description.
The Vascular Endothelial Growth Factor (VEGF) is a key molecule in angio-
genesis, since it stimulates the migration, proliferation and survival of endothelial
cells [ 44 , 45 ]. The signaling pathways downstream its main receptor, the VEGFR-2 is
well described in the literature [ 46 , 47 ], and we can find mathematical models of the
binding of VEGF to its receptor. For example, Alarcòn and coworkers have devel-
oped a stochastic model of the receptor dimerization and activation [ 48 ]. However,
none of those models goes further than the binding of VEGF to its receptor.
A global view and comprehension of the intracellular pathways of VEGFR2 can
be achieved based on information available in recent literature and specialized
databases. Tools such as PubMed and Kyoto Encyclopedia for Genes and Genomes
(KEGG1) are important to achieve this goal. Figure 4 shows a diagram of the
VEGFR2 intracellular signaling pathways built based on the available information.