Biomedical Engineering Reference
In-Depth Information
Cell death, quiescence and proliferation are determined by a cell's internal
protein concentrations. We apply the following rules to identify the different cell
states and show their application for a particular cell
i
(intracellular concentrations
of the cell
i
are denoted by [
](
i
)). In normal cells, cell death occurs if [p53]
(
i
)
p53
THR
(
i
), where p53
THR
(
i
) is the maximal threshold they can sustain before
undergoing apoptosis, and is given by
>
(
p53
high
THR
for
r
normal
ð
i
Þ >r
THR
p53
THR
ð
i
Þ¼
:
(3.8)
p53
low
THR
for
r
normal
ð
i
Þr
THR
We define the set of cells in the neighbourhood of cell
i
as
Y
i
. The normal cell ratio
in (
3.8
) is given by
P
k2Y
i
normal cells at site
k
r
normal
ð
i
Þ¼
P
k2Y
i
normal or cancer cells at site
k
:
(3.9)
Definition (
3.9
) accounts for the fact that healthy cells are more likely to die if they
live in a tumour environment. This can be caused by the altered microenvironment
in tumours. Tumour cells enter quiescence if [p27](
i
)
>
p27
e
or leave quiescence if
[p27](
i
)
T
death
), the cell
dies. It should be noted that cancer cell death is not influenced by p53.
The condition to be satisfied for the proliferation of cells is
<
p27
l
. If a cancer cell is in quiescence for too long (
>
½
Cdh1
ð
i
Þ<
Cdh1
THR
and
½
cycCDK
ð
i
Þ>
cycCDK
THR
:
(3.10)
The daughter cell is placed in the current location if there is free space; otherwise, it
is moved to an empty neighbour location with a high oxygen concentration. If there
is no free space in the neighbour CA-cells, the parent cell dies and no daughter is
produced.
3.2.2 Cellular Layer
The following section focuses on the creation and movement of new vessels. For a
detailed description, see Owen et al. [
20
]. New sprouts form at site
i
(which must be
a vessel site) with probability
sprout
i
p
where
P
sprout
max
c
VEGF
V
sprout
þ
sprout
i
p
¼
c
VEGF
D
t
;
(3.11)
with the timestep size
Dt
. Since VEGF stimulates sprout formation, the probability
of sprouting is assumed to increase with the VEGF concentration,
c
VEGF
. The
maximum sprouting probability is
P
max
sprout
, and
V
sprout
is a constant. New sprouts
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