Biomedical Engineering Reference
In-Depth Information
f
1
(t)
q
3
K
31
K
12
q
1
q
2
K
21
K
20
FIGURE 7.39
Illustration for Exercise 69.
72.
Consider the three-compartment model shown in Figure 7.20 with nonzero parameters and
inputs
K
12
¼
0
:
4,
K
10
¼
0
:
5,
K
21
¼
0
:
6,
K
31
¼
0
:
9,
K
32
¼
0
:
7,
K
23
¼
0
:
2,
K
13
¼
0
:
8, and
f
2
ð
t
Þ¼
5
Assume that the initial conditions are zero. Write a single differential equation involving
the input and only variable (a)
u
ð
t
Þ:
q
3
.
(g) Using SIMULINK, simulate the system from the original set of differential equations and
graph
q
1
;(b)
q
2
;(c)
q
3
.For
t
>
0, solve the system for (d)
q
1
;(e)
q
2
;(f)
q
3
.
73.
Consider the three-compartment model shown in Figure 7.20 with nonzero parameters and
inputs
q
1
,
q
2
,and
K
¼
0
:
6,
K
¼
0
:
2,
K
¼
0
:
3,
K
¼
0
:
5,
K
¼
0
:
6,
K
¼
0
:
4,
K
¼
0
:
8, and
f
ð
t
Þ¼
12
20
21
31
32
23
13
1
2
Assume that the initial conditions are zero. Write a single differential equation involving
the input and only variable (a)
u
ð
t
Þ:
q
3
.
(g) Using SIMULINK, simulate the system from the original set of differential equations and
graph
q
1
;(b)
q
2
;(c)
q
3
.For
t
>
0, solve the system for (d)
q
1
;(e)
q
2
;(f)
q
3
.
74.
Consider the three-compartment model shown in Figure 7.20 with nonzero parameters and
inputs
q
1
,
q
2
,and
K
12
¼
0
:
3,
K
20
¼
0
:
4,
K
21
¼
0
:
8,
K
31
¼
0
:
5,
K
32
¼
0
:
3,
K
23
¼
0
:
4,
K
13
¼
0
:
8,
f
1
ð
t
Þ¼
3dð
t
Þ
,
Assume that the initial conditions are zero. Write a single differential
equation involving the input and only variable (a)
and
f
3
ð
t
Þ¼
3
u
ð
t
Þ:
q
1
;(b)
q
2
;(c)
q
3
.For
t
>
0, solve the system for
(d)
q
3
. (g) Using SIMULINK, simulate the system from the original set of differential
equations and graph
q
1
;(e)
q
2
;(f)
q
3
.
75.
Consider the three-compartment model shown in Figure 7.20 with nonzero parameters and
inputs
q
1
,
q
2
,and
K
12
¼
0
:
6,
K
20
¼
0
:
2,
K
21
¼
0
:
3,
K
31
¼
0
:
5,
K
32
¼
0
:
6,
K
23
¼
0
:
4,
K
13
¼
0
:
8, and
f
2
ð
t
Þ¼
dð
t
Þþ
Assume that the initial conditions are zero. Write a single differential equation
involving the input and only variable (a)
5
u
ð
t
Þ:
q
1
;(b)
q
2
;(c)
q
3
.For
t
>
0, solve the system for (d)
q
1
;
(e)
q
3
. (g) Using SIMULINK, simulate the system from the original set of differential
equations and graph
q
2
;(f)
q
3
.
76.
Consider the mammillary three-compartment model shown in Figure 7.21 with nonzero
parameters and inputs
q
1
,
q
2
,and
ð
t
Þ:
Assume that the initial conditions are zero. Write a single differential equation involving the
K
12
¼
0
:
3,
K
10
¼
0
:
5,
K
21
¼
0
:
2,
K
23
¼
0
:
4,
K
32
¼
0
:
6, and
f
2
ð
t
Þ¼
5d
