Biomedical Engineering Reference
In-Depth Information
Figure 3
. Initial levels of mechanical confinements in a 50 × 50 square grid lattice. The
XY axes correspond to the spatial coordinates of the grid locations. The center of the
pressure "crater" is placed at coordinates (
x
= 25,
y
= 25). The vertical color bar on the
right shows the
grayscale
used to measure the intensity of mechanical pressures.
pressure corresponds to the site of the second nutrient source at the NE quadrant
(Figure 2). Thus, in effect, the second nutrient source is "defended" by higher
mechanical confinements, representing a normal blood vessel within a noncan-
cerous parenchymal environment. Our subsequent works assume that, outside of
the low-pressure crater, mechanical confinements are distributed randomly in a
uniform manner. Figure 3 illustrates the initial levels of mechanical confine-
ments as assumed in (7) and (8).
5.1.3. Toxicity
The initial levels of toxicity can be assumed to be zero everywhere on the
lattice (6-8), or we can introduce an initial uniform distribution of hypoxia that
is already in the system from the beginning (9).
Hypoxia
(due to limitation of
oxygen diffusion in tissue) is known to be an important component of tumor
biology. For example, it has been shown that the growth of multicellular sphe-
roids is adversely affected by diffusion-limited
p
O
2
(49). Our "initial hypoxia"
setup was inspired by the fact that locations farther away from blood vessels
