Biomedical Engineering Reference
In-Depth Information
•
Calculation of cell cycle, p53 and VEGF ODEs (subcellular layer)
The
subcellular layer is coupled to its local environment via the oxygen concen-
tration. Oxygen drives the cell cycle of individual cells, whose current state is
described by the time-dependent concentrations of the proteins Cdh1,
cycCDK, p27, npRB and the cell mass
M
. Internal p53 and VEGF
concentrations are also considered. All subcellular variables are modelled
by the coupled systems of non-linear ODEs (
3.1
)-(
3.7
).
•
Check for cell division (cellular layer)
Cells divide if their Cdh1 and
cycCDK concentrations are under, respectively, over a predefined threshold
[see (
3.10
)].
•
Cell movement (cellular layer)
Vascular tip cells perform a biased random
walk through the tissue. The probability of moving in a certain direction is
influenced by the local VEGF gradient and cell densities [see (
3.12
)].
The motility of normal and cancer cells is also included via (
3.12
).
•
Calculation of VEGF concentration (diffusible layer)
Quiescent tumour
cells and hypoxic normal cells produce VEGF, and so contribute to the source
term in the reaction-diffusion equation (
3.15
) for the VEGF concentration
c
VEGF
(
t
,
x
). VEGF is removed by the vascular system.
•
Check for cell quiescence (cellular layer)
Tumour cells enter or leave
a quiescent state depending on the internal cell p27 concentration, which
is described in (
3.4
). Oxygen is the external factor that
influences the
level of p27.
•
Check for cell death (cellular layer)
Normal cells die if their subcellular
p53 concentration exceeds a threshold value. If a normal cell is surrounded by
a high number of tumour cells, then its p53 threshold for cell death is
reduced [see (
3.8
)]. This models the degradation of a tumour's environment
by tumour cells. Tumour cells die if they are quiescent for a certain period
of time; unlike normal cells, their death is not influenced by p53.
3.
Update vasculature (cellular and vascular layer)
The vascular system continu-
ally remodels and evolves in response to external and internal stimuli:
•
Check for new tip cells (cellular layer)
A raised VEGF concentration in the
tissue stimulates the vasculature to form new sprouts. The probability that
new sprouts emerge is specified by (
3.11
) and is an increasing function of the
local extracellular VEGF concentration.
•
Check for anastomosis (cellular layer)
New vessels are formed if sprouts
connect to other sprouts or to the pre-existing vascular network.
•
Vessel pruning (vascular layer)
Vessels that are underperfused (
t
w
< t
crit
)
for a certain period of time (
T
prune
) are removed from the vascular network.
•
Calculation of radius adaptation (vascular layer)
The vessel radii are
updated at each timestep according to (
3.21
). The change in vessel radii is
influenced by haemodynamic and metabolic stimuli as well as the general
tendency of vessels to shrink [see (
3.22
)-(
3.25
)].
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