Biomedical Engineering Reference
In-Depth Information
9.
For the reaction given in Eq. (8.25) and with
q
A
ð
0
Þ¼
10,
q
B
ð
0
Þ¼
10,
q
P
ð
0
Þ¼
0,
K
1
¼
0
:
5,
K
1
¼
0
:
3, a ¼
3, and b ¼
2, simulate the solution for
q
P
:
10.
For the reaction given in Eq. (8.27) and with
q
A
ð
0
Þ¼
15,
q
B
ð
0
Þ¼
0,
q
P
ð
0
Þ¼
0,
K
1
¼
8, and
K
2
¼
3, solve and simulate the solution for
q
A
,
q
B
and
q
P
:
Compare these results with the quasi-
steady-state solutions.
11.
For the reaction given in Eq. (8.27) and with
q
A
ð
0
Þ¼
25,
q
B
ð
0
Þ¼
0,
q
P
ð
0
Þ¼
0,
K
1
¼
2, and
K
2
¼
10, solve and simulate the solution for
q
A
,
q
B
and
q
P
:
Compare these results with the quasi-
steady-state solutions.
12.
For the reaction given in Eq. (8.27) and with
q
A
ð
0
Þ¼
10,
q
B
ð
0
Þ¼
0,
q
P
ð
0
Þ¼
0,
K
1
¼
5, and
K
2
¼
20, solve and simulate the solution for
q
A
,
q
B
and
q
P
:
Compare these results with the quasi-
steady-state solutions.
13.
Generate the solutions for Figures 8.3 and 8.4.
14.
Simulate the reaction given in Eq. (8.33) and compare with the quasi-steady-state approximation
for
q
S
,
q
E
,
q
ES
and
q
P
:
Assume that
K
1
¼
5,
K
1
¼
0
:
3,
K
2
¼
1,
q
S
ð
0
Þ¼
9,
q
E
ð
0
Þ¼
0
:
01,
q
ES
ð
0
Þ¼
0,
:
15.
Simulate the reaction given in Eq. (8.33) and compare with the quasi-steady-state approximation
for
and
q
P
ð
0
Þ¼
0
q
S
,
q
E
,
q
ES
and
q
P
:
Assume that
K
1
¼
1,
K
1
¼
0
:
1,
K
2
¼
5,
:
16.
Simulate the reaction given in Eq. (8.33) and compare with the quasi-steady-state approximation
for
q
S
ð
0
Þ¼
20,
q
E
ð
0
Þ¼
0
:
008,
q
ES
ð
0
Þ¼
0, and
q
P
ð
0
Þ¼
0
q
S
,
q
E
,
q
ES
and
q
P
:
Assume that
K
1
¼
10,
K
1
¼
1,
K
2
¼
3,
q
S
ð
0
Þ¼
30,
q
E
ð
0
Þ¼
1,
q
ES
ð
0
Þ¼
0,
:
17.
Given the model in Eq. (8.51) and with
and
q
P
ð
0
Þ¼
0
q
S
ð
0
Þ¼
10,
V
max
¼
25,
K
M
¼
5, and
f
ð
t
Þ¼
5d
ð
t
1
Þ
,
q
S
:
18.
Given the model in Eq. (8.51) and with
simulate the solution for
q
S
ð
0
Þ¼
50,
V
¼
5,
K
M
¼
1, and
f
ð
t
Þ¼
u
ð
t
Þ
u
ð
t
1
Þ
,
max
q
S
:
19.
Given the model in Eq. (8.51) and with
simulate the solution for
e
t
,
q
S
ð
0
Þ¼
25,
V
max
¼
10,
K
M
¼
3, and
f
ð
t
Þ¼
5
q
S
:
20.
Given the model in Eq. (8.51) and with
simulate the solution for
q
S
ð
0
Þ¼
10,
V
max
¼
25,
K
M
¼
5, and
f
ð
t
Þ¼
5dð
t
1
Þ
,
q
S
:
21.
Simulate the model in Eq. (8.66) given that
simulate the solution for
K
12
¼
3,
K
21
¼
1,
V
max
¼
10,
K
M
¼
1,
K
10
¼
0,
and
K
20
¼
0
:
02
:
The inputs are
f
1
ð
t
Þ¼
4dð
t
Þ
and
f
2
ð
t
Þ¼
0
:
The initial conditions are zero.
22.
Simulate the model in Eq. (8.66) given that
K
12
¼
3,
K
21
¼
2,
V
max
¼
20,
K
M
¼
2,
K
10
¼
0,
and
K
20
ð
0
Þ¼
0
:
The inputs are
f
1
ð
t
Þ¼
4
ð
u
ð
t
Þ
u
ð
t
10
Þ
Þ
and
f
2
ð
t
Þ¼
3
ð
u
ð
t
1
Þ
u
ð
t
6
Þ
Þ:
The
initial conditions are zero.
23.
Simulate the model in Eq. (8.67) given that
K
12
¼
0
:
25,
K
21
¼
3,
V
max
¼
30,
K
M
¼
5,
K
10
¼
0,
and
K
20
ð
0
Þ¼
0
:
2
:
The inputs are
f
1
ð
t
Þ¼
2
u
ð
t
Þ
and
f
2
ð
t
Þ¼
3
u
ð
t
Þ:
The initial conditions are zero.
24.
Simulate the model in Eq. (8.67) given that
K
12
¼
2,
K
21
¼
3,
V
max
¼
40,
K
M
¼
8,
K
10
¼
0,
e
:03
t
u
ð
t
Þ:
and
K
20
ð
0
Þ¼
0
:
2
:
The inputs are
f
1
ð
t
Þ¼
5
u
ð
t
Þ
and
f
2
ð
t
Þ¼
3
The initial conditions are
zero.
25.
Simulate the model in Eq. (8.67) given that
K
12
¼
3,
K
21
¼
2,
V
max
¼
10,
K
M
¼
0
:
8,
K
10
¼
0
:
1,
K
20
ð
0
Þ¼
0
:
3
:
The inputs are
f
1
ð
t
Þ¼
4
u
ð
t
Þ
and
f
2
ð
t
Þ¼
0
:
The initial conditions are zero.
and