Biomedical Engineering Reference
In-Depth Information
differentiation and proliferation rates. Yet any attempt to eliminate CSCs must
take into consideration the feedback of the CSC population on itself. For example,
elimination of DCs may accelerate the CSC replication rate, owing to the negative
feedback that CSCs receive from the population. Hence, cancer therapy based on
targeting only DCs (or progenitor tumor cells) may be counterproductive, as it may
stimulate CSC proliferation.
To analyze the dynamics of cancer cell populations containing CSCs, Vainstein
et al. [
90
] adapted the SC model by Agur and colleagues, under the CSC theory
assumption that hierarchical dynamics in cancer resemble those of normal tissues.
Several changes were made in an attempt to increase the model's realism. In Vain-
stein et al.'s model, a CSC can be in a non-cycling (quiescent) state, or in a cycling
state, in which a proliferation process takes place. Furthermore, whereas the original
model described proliferation as a “decision” of an empty space to become occupied
by an SC, in this model proliferation is initiated by the proliferating cell (i.e., the
internal counter for proliferation belongs to the dividing cell and not to the vacant
space). Finally, the model is probabilistic, where QS control is achieved by setting
the probability of differentiation and of entering proliferation cycle as a function of
the number of stem and vacant neighbor cells, respectively.
The model is implemented in a honeycomb-shaped CA grid, where each
automata cell has six neighbors. The probability
p
d
of a non-cycling CSC
A
to
differentiate is
a
m
(
−
)
p
max
p
min
p
d
=
p
max
−
den
m
(5)
a
m
+
(
A
)
N
2
2
k
is the density of SCs in the proximity of
A
,
N
i
being
the number of CSCs at a distance
i
from
A
,and
k
is the damping coefficient
reflecting a reduction in signal intensity as the distance from the neighbor grows.
1
where den
(
A
)=
N
1
+
a
represents the sensitivity to this microenvironmental signal, and
m
,
p
max
and
p
min
are parameters for steepness and maximal and minimal borders of the function,
respectively.
The probability
p
c
of a non-cycling CSC A to enter the proliferation cell cycle is
/
n
p
c
=
1
−
(
1
−
p
0
)
,
(6)
where
n
is the number of vacant automata cells in the proximity of
A
, calculated
in the same way as
den
,and
p
0
is a parameter representing the proliferation
probability when one neighboring vacant cell is available. When a CSC enters
the cell cycle, an adjacent empty cell is randomly chosen, and after a certain
proliferation time
(
A
)
this site becomes occupied by a new CSC. As in the previous
models [
3
,
4
], DCs possess an internal counter as well, to force their death after an
estimated life span
Θ
.
The model was simulated under many different combinations of model parameter
values, in biologically plausible ranges based on published information (see [
90
]
for details). These model parameters include parameters determining a CSC's level
Φ
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