Biomedical Engineering Reference
In-Depth Information
In other words, the change in the level of toxicity at time
t
, U
t,j
, is due to (i) dif-
fusing toxicity from the surrounding regions, /#(
D
U
/U), where
D
U
is the diffusion
coefficient of toxic metabolites, and augmented by (ii) the rate of toxic accumu-
lation,
r
U
, multiplied by the population of tumor cells in that location, I
j
. The last
term thus contains the assumption that a greater population of tumor cells leads
to faster accumulation of toxic metabolites. In fact, (42) has shown that in
EMT6-cells detrimental accumulation of toxicity in the form of lactic acid re-
sults in inhibition of onsite proliferation. Yet at the same time, the authors of
(43) found that higher toxic levels can also stimulate active migration of tumor
cells, and that, although hypoxia induces growth arrest in ovarian carcinoma
cells, they still exert proteolytic (Type IV collagenase) activity, which is re-
quired to maintain their invasive properties. Similarly, (44) described recently a
hypoxia-induced migration of human U-138MG glioblastoma cells using an in-
vivo model. Together, these studies indicate that migration is stimulated when
onsite accumulation of toxicity acts as repulsion, ultimately forcing tumor cells
out of their current location.
4.
SPECIFICATIONS OF THE MODEL
In recent work, we have extended the "core" agent-based modeling platform
above to examine specific scientific questions.
4.1. Search Mechanism
In (6), we propose the concept of
global vs. local
search. This theoretical
notion represents the existence of two different cell-surface receptors directing
the chemotactic movement of virtual tumor cells with two distinctively different
lower signal detection thresholds (or with two distinct intracellular amplification
strengths). The first type of receptor, employed during global search, can be
thought of exhibiting a lower signal detection threshold and as such is more sen-
sitive to diffusive signals emitted from distant locations. On the other hand, the
second type of receptor (involved during local search) exhibits an elevated level
of the lower signal detection threshold and thus is arguably employed to capture
stronger signals coming from the local neighborhood of a cell's current location.
The potential tradeoff between global and local search is captured by the pa-
rameter
r
S
. Smaller values of
r
S
imply lower energy costs of spatial movement, S
(see Eq. [4]), and thus increase the scope of global search by conferring higher
mobility to tumor cells. In contrast, larger values of
r
S
promote a shift toward a
more local search in the neighborhood of the cells' original location due to the
higher costs of spatial movement in terms of energy expenditures.
