Biomedical Engineering Reference
In-Depth Information
Fig. 4
Treatment combinations. Scatter plot of the numerical solution of system (
5
). The values
plotted correspond to the cancer cell counts at day 2000 and they are classified by color:
green
-
clearance (no cancer),
blue
-partial clearance (cancer below the initial condition of 10
3
),
red
-small
growth (from 10
3
to 10
6
),
black
-large growth (above 10
6
). The
x
and
y
axes represent the six
combinations of the four
treatment parameters c
as sampled in the LHS
described in the
Numerical simulations
section. We vary all four inputs simultaneously (sampling
from uniform distributions within their respective ranges) and keep the rest of the parameters
constant to the baseline values shown in Table
1
(
Baseline
column)
(
t
)
,
s
1
(
t
)
,
a
(
t
)
,
r
2
(
t
)
x 10
4
Baseline
Immune cells
Tumor cells
Cl
earance (conditions (15) satisfied
)
Immune cells
Tumor cells
Cle
arance (conditions (15) not satisfi
ed)
Immune cells
Tumor cells
6
10000
5000
9000
4500
5
8000
4000
7000
3500
4
6000
3000
3
5000
2500
4000
2000
2
3000
1500
2000
1000
1
1000
500
0
0
0
0
500
1000
1500
2000
0
2
4
6
8
10
0
200
400
600
days
days
days
Fig. 5
Numerical solutions of system (
5
). Shown are plots for the baseline simulation (Parameters
are chosen from the
Baseline
column in Table
1
), for clearance when conditions (
15
) are satisfied
(values of the treatment parameters are:
s
1
(
t
)=
764.5072,
r
2
(
t
)=
0.0023,
a
(
t
)=
38.0040,
c
0.3710), and clearance where conditions (
15
) are not satisfied (values of the treatment
parameters are:
s
1
(
(
t
)=
10
2
t
)=
,
r
2
(
t
)=
0.0523,
a
(
t
)=
2,
c
(
t
)=
0.05). The rest of the parameters
are set to baseline values shown in Table
1
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