Biomedical Engineering Reference
In-Depth Information
Fig. 3 Illustration of the multiscale tumor growth and angiogenesis model integrating tumor
regulation box and VEGF signaling-endothelial cells compartment. Adapted from [ 38 ]
can for instance refer to [ 36 , 37 ]. These models incorporate a large number of
parameters that do not have a biological meaning or are hardly measured exper-
imentally, making model calibration a challenging issue. Finally, the models we
are going to discuss in this paragraph are continuous model as they describe the
evolution of continuous variable such as tumor size and density of blood vessels or
endothelial cells. Many multiscale models are developed using discrete formalisms
focusing on individual cell behaviors and integrating a population of cells to
constitute a whole vascularized virtual tumor. Those aspects were previously
discussed in the chapter by Boas et al.
We will shortly describe a model based on a set of partial differential equations
that describe the behavior of endothelial cells, which constitute blood vessel walls,
tumor cells, as well as of some major proangiogenic substances, such as the vascular
endothelial growth factor (VEGF). This model can be viewed as an assembly of two
major pieces that occur at different spatial scales. The first one is similar to the model
presented in Fig. 2 : it describes the regulation of tumor tissue as proliferative, qui-
escent and necrotic tissue. Hypoxic tumor cells are assumed to secrete VEGF, which
in turns will bind the VEGFR2 receptors of endothelial cells constituting the vessels.
The second one is the dynamics of the vascular network where the endothelial cell
behavior, namely proliferation, migration and survival, is driven by intracellular
signaling of VEGFR2 receptor. The proposed model consists of 11 equations and 45
Search WWH ::




Custom Search