Biomedical Engineering Reference
In-Depth Information
Angiogenesis is induced by hypoxic tissue which, for example, can be a tumor or
an active muscle. The change in oxygen and nutrient supply due to the new
vasculature changes the signals coming from the tissue, resulting in a dynamic
feedback loop between angiogenesis and the needs of the tissue. Also blood flow
may be key to this feedback. Disfunctional vessels are not able to support blood
flow and do not contribute to the perfusion of the tissue. Endothelial cells change
their behavior due to the shear stresses induced by blood flow [
31
]. The inclusion
of these processes in a multi-scale angiogenesis model would be a great tool to
study whether pathological processes either involve excessive or insufficient blood
vessel growth. Such multi-scale models can not only be used to formalize and
validate hypotheses, they can also be used to predict the effects of pro- or anti-
angiogenic therapies on the vasculature and the other tissues involved.
In order to build these multi-scale models, researchers often extend existing
models. For example, the particle-based sprouting model by Anderson et al. [
6
] has
been extended with blood flow [
32
]. This model suggested that most vessels are not
perfused due to the lack of anastomosis, and thus drugs can not reach the target.
More complex approaches have been used to combine more detailed angiogenesis
models with blood flow and the kinetics of oxygen and VEGF [
33
-
35
]. This model
has show to produce vascularization similar to experimental observation in a het-
erogeneous extracellular matrix [
34
] and in the skeletal muscle [
36
].
In the previous models the surroundings of the vasculature are static and are not
being changed by the growing vessels and the increasing supply of oxygen and
nutrients. This means that a part of the feedback is missing, for example a tumor
can grow when the blood supply increases and a larger tumor needs a bigger
supply of blood. Shirinifard et al. [
37
] combined cell-based Cellular Potts models
(see
Sect. 3.1
) of blood vessel formation and tumor growth to investigate how
tumor growth and vascular remodeling interact. This high level of detail gives
insight in how specific cell properties influence tumor growth and angiogenesis.
Cell-based modeling would be a suitable approach to create predictive multi-
scale models. Cell behavior in such a model must be linked to biological or
physical cell properties. The extracellular matrix as well as blood flow could be
added to the model. Then, the cell properties could be linked to matrix interactions
and local levels of oxygen, nutrients and other chemicals. A cell-based model
could simulate emergent angiogenesis and blood vessel remodeling and could be
used to predict the effects of therapeutic agents.
3 Cell-Based Model of In Vitro Sprouting
The previous section discussed how multi-level computational models aim to fuse
models to incorporate different aspects of angiogenesis, such as cell behavior,
matrix interactions and blood flow. Processes like chemotaxis and haptotaxis can
be described with continuum models, while we argued that the representation of
cells requires a cell-based approach. Cell-based models explicitly model cell
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