Biomedical Engineering Reference
In-Depth Information
of tumor cells toward these EGF signals is facilitated by the cells' specific epi-
dermal growth factor receptor (EGFR), known to be overexpressed in primary
human glioblastomas (34). In the case of glucose, tumor cells convert their nu-
trient uptake to lactic acid. Thus, relative to normal tissue, tumor tissues are of-
ten found to experience a several-fold increase in both glucose uptake and lactic
acid production (35,36). The result of the escalating production of lactate and
hydrogen ions is a thin layer of an acidic environment that surrounds tumor cell
colonies. For example, (37) reports decreasing levels of pH, while (38) reports
decreasing levels of
p
O
2
on the surface of tumor spheroids. Both the lower level
of
p
O
2
and the reduced pH should render the microenvironment less viable and
thus less "attractive." Finally, mechanical confinements in our model represent
the stress or pressures exerted by the surrounding tissues, which hampers the
ability of tumor cells to grow and invade the parenchyma. Experimentally, a
number of studies have shown that these mechanical properties of the tissue
environment indeed influence both the proliferating and migratory behavior of
tumor cells (39, 40).
3.2.1. Proliferation
Either proliferation or migration of tumor cells is allowed to occur if a
number of criteria are fulfilled. The algorithm proceeds as follows. First, for
every viable tumor cell, we determine whether its location
j
belongs to a "le-
gitimate" tumor cluster (see ยง3.1.2 above for details). If the tumor cell does not
reside in a cluster, then it is eligible to either proliferate or migrate, though not
both. If, on the contrary, the cell is a member of a cluster, then we next check
whether the tumor cell is located on the surface of a cluster. If the "cluster sur-
face" condition is satisfied, a tumor cell can proliferate if its onsite levels of nu-
trients and toxic metabolites are within certain demarcating thresholds (see
Figure 1). Let G
j
and U
j
denote site
j
's level of nutrients and toxic metabolites,
respectively. Then proliferation may occur if the level of nutrients is higher than
the upper nutrient threshold, G
j
> G
U
, while at the same time, the level of toxic
metabolites is below the lower toxicity threshold, U
j
< U
L
.
Even if the environmental conditions are favorable (i.e., high nutrients and
low toxicity), there is still a chance that proliferation will fail to occur. We
model this element of stochasticity by assuming that the probability to prolifer-
ate is proportional to the onsite levels of nutrients:
Pr
proliferate,
j
= G
j
/ (G
j
+
k
prolif
),
[1]
where
k
prolif
represents a parameter that controls the likelihood of cell prolifera-
tion. Higher
k
prolif
implies a lower
probability
to proliferate because it is inversely
proportional to the capability of tumor cells to proliferate. Equation [1] states
