Biomedical Engineering Reference
In-Depth Information
of a thin epithelium made only of connected cells and in the absence of convective
mass transfer:
rate of change of cell density
=
cell migration
+
cell proliferation
−
cell death
,
(11.1)
rate of change of activator concentration
=
activator diffusion
+
activator synthesis
−
activator degradation
.
(11.2)
rate of change of inhibitor concentration
=
inhibitor diffusion
+
inhibitor synthesis
−
inhibitor degradation
.
(11.3)
The change rate in cell density (
n
) depends on the cell migration flux and
production and loss rates. The death rate is supposed to be proportional to the cell
density. The controlled cell proliferation takes into account the cell density (
n
0
)and
regulator concentration (
c
0
) in the unwounded state. The proliferation model states
that [
1476
]:
= P
n
2
n
n
0
−
cell proliferation
(11.4)
(
P =
P
(
)
: chemically controlled cell division rate)
The time gradient of substance concentration (
c
) depends on the chemical
diffusion flux and its production and decay rates. The role of blood flow in the
transport of cells and compounds is ignored. The temporal decay of an active
compound is currently assumed to be governed by fisrt-order kinetics modeled by a
rate constant
c
−
τ
c
. The production (
p
) of the regulator (subscript
r
), assuming that
p(
)=
τ
α
, which is related to the maximal rate
of regulator production, can be given by [
1476
]:
n
0
c
0
and introducing a parameter
n
0
+
α
2
for an activator
2
n
n
0
p
r
(
n
)=
τ
c
0
,
(11.5)
n
2
+
α
n
n
0
=
τ
.
c
0
for an inhibitor
(11.6)
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