Biomedical Engineering Reference
In-Depth Information
X 10
-9
4
W
diss
W
p
with W
P
=7.10
-7
g/(cm. sec
3
)
W
p
with W
P
=9.10
-7
g/(cm. sec
3
)
W
p
with W
P
=11.10
-7
g/(cm. sec
3
)
W
p
with W
P
=13.10
-7
g/(cm. sec
3
)
3.5
3
2.5
2
1.5
1
0.5
0
800
1000
1200
1400
1600
1800
2000
Fig. 1
W
diss
and
W
prod
for different values of
w
P
σ
∗
=
10
−
10
erg/s. On the basis of the following
formula derived by equating dissipated power and produced power:
0
.
28 mM, we calculated
W
diss
=
6
.
2
·
W
diss
ν
−
1
V
P
v
cell
w
cell
=
,
(43)
3
R
3
P
is the volume of the proliferat-
4
where
v
cell
is the cell volume and
V
P
=
−
ρ
ing rim, we estimated for the quantity
w
P
=
v
cell
, namely the power supplied
by proliferating cells per unit cell volume, the value
w
P
=
w
cell
/
10
−
7
g/(cm s
3
).
If we now apply our conjecture that this value represents a characteristic of the
proliferating cells of that cell line, and so is irrespective of the spheroid size, then
we can use Eq. (
43
) (with the estimated
w
cell
,and
W
diss
(
9
.
05
·
)
as the equation determining the spheroid radius
R
for values of the outer oxygen
concentration
R
)=
W
C
(
R
)+
W
E
(
R
)
σ
∗
different from 0
28 mM. As a sensitivity test, in our simulation we
checked that increasing the estimated
w
P
value by 20 % makes
R
decrease by 10 %.
In Fig.
1
we plot
W
diss
and
W
prod
as functions of
R
, for different values of
w
P
.
Tab le
2
shows the values of
R
for different values of
.
σ
∗
, deduced by means of the
10
−
7
g/(cm s
3
criterion illustrated above and assuming
w
P
=
9
·
)
), compared to the
experimental values in [
32
].
Search WWH ::
Custom Search