Biomedical Engineering Reference
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and treatment strategies in near future. Continuum based models can be
used to predict the evolution of tumors boundary time and this knowledge
may in turn help estimate the eect that various methods of treatment,
for example, chemotherapy and ultrasound, may have on the tumor be-
havior as well as on the ECM and ultimately on the host. A continuous
based mathematical model can also be used how hypoxia is a promoter of
angiogenesis. A model taking account of the main components, that is, tu-
mor size, vessel density, oxygen concentration, anti-angiogenic factors and
pro-angiogenic factors could predict the likelihood of angiogenesis of dier-
ent congurations. Thus the model can be validated against experimental
measurements.
6. Cellular scale models of growth of solid tumors
The cellular scale refers to the main (interactive) activities of the cells:
activation and proliferation of tumor cells and competition with immune
cells. More specically, one has
(i) Fast proliferation of tumor cells, which are often degenerated endothe-
lial cells, takes place when an environmental cell loses its death program
and/or starts undergoing mitosis without control.
(ii) Competition with the immune system starts when tumor cells are rec-
ognized by immune cells, resulting either in the destruction of tumor
cells or in the inhibition and depression of the immune system.
(iii) After dierentiation tumor cells undergo a process of maturation, which
makes them more and more proliferative and aggressive toward the en-
vironment and the immune system. Tumor cells can be additionally
activated towards proliferation by nutrient supply from the environ-
ment.
(iv) Activation and inhibition of the immune cells in their competition with
tumor cells are regulated by cytokine signals. These interactions, de-
veloped at the cellular level, are ruled by processes which are performed
at the subcellular scale.
(v) Activation and inhibition of cells belonging to the tumor and to the
immune system can also be induced by a properly addressed medical
treatment.
A model developed at the microscopic scale denes the time evolution of
the physical state of a single cell. Often these models are stated in terms of
ordinary dierential equations. On the other hand, if we aim to describe the
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