Biomedical Engineering Reference
In-Depth Information
(b)
q
2
. (e) Using SIMULINK, simulate the system
from the original set of differential equations and graph
q
2
. For
t
>
0, solve the system for (c)
q
1
; (d)
q
1
and
q
2
.
e
2
t
u
ð
t
Þ
64.
The input to the compartmental system in Figure 7.38 is 0
:
5
. The transfer rates are
K
20
¼
0
:
3,
K
21
¼
1
:
0, and
K
12
¼
0
:
6
:
The initial conditions are
q
1
0
ðÞ¼
0 and
q
2
0
ðÞ¼
4
:
Write a
single differential equation involving the input and only variable (a)
q
1
; (b)
q
2
. For
t
>
0, solve
the system for (c)
q
2
. (e) Using SIMULINK, simulate the system from the original set of
differential equations and graph
q
1
; (d)
q
2
.
65.
The input to the compartmental system in Figure 7.38 is 0
q
1
and
e
2
t
2
ð
Þ
:
5
u
ð
t
2
Þ
. The transfer rates
are
K
20
¼
0
:
3,
K
21
¼
1
:
0, and
K
12
¼
0
:
6
:
The initial conditions are
q
1
0
ðÞ¼
0 and
q
2
0
ðÞ¼
0
:
Write a single differential equation involving the input and only variable (a)
q
1
; (b)
q
2
. For
t
>
0, solve the system for (c)
q
2
. (e) Using SIMULINK, simulate the system from the
original set of differential equations and graph
q
1
; (d)
q
2
.
66.
The input to the compartmental system in Figure 7.38 is 0
q
1
and
e
2
t
u
ð
t
Þ
e
2
t
1:5
ð
Þ
:
5
0
:
5
u
ð
t
1
:
5
Þ
.
The transfer rates are
K
20
¼
0
:
3,
K
21
¼
1
:
0, and
K
12
¼
0
:
6
:
The initial conditions are
q
1
0
ðÞ¼
0
and
q
2
0
ðÞ¼
0
:
Write a single differential equation involving the input and only variable (a)
q
1
;
(b)
q
2
. (e) Using SIMULINK, simulate the system
from the original set of differential equations and graph
q
2
. For
t
>
0, solve the system for (c)
q
1
; (d)
q
1
and
q
2
.
67.
The input to the compartmental system in Figure 7.38 is 3 cos 4
tu
ð
t
Þ
. The transfer rates are
K
20
¼
0
:
3,
K
21
¼
1
:
0, and
K
12
¼
0
:
6
:
The initial conditions are
q
1
0
ðÞ¼
0 and
q
2
0
ðÞ¼
0
:
Write a
single differential equation involving the input and only variable (a)
q
1
; (b)
q
2
. For
t
>
0, solve
the system for (c)
q
2
. (e) Using SIMULINK, simulate the system from the original set of
differential equations and graph
q
1
; (d)
q
2
.
68.
The input to the compartmental system in Figure 7.38 is 3 sin 2
q
1
and
tu
ð
t
Þ
. The transfer rates are
K
¼
3,
K
¼
5, and
K
¼
7
:
The initial conditions are
q
1
0
ðÞ¼
1 and
q
2
0
ðÞ¼
0
:
Write a single
20
21
12
differential equation involving the input and only variable (a)
q
1
; (b)
q
2
. For
t
>
0, solve the
system for (c)
q
2
. (e) Using SIMULINK, simulate the system from the original set of
differential equations and graph
q
1
; (d)
q
2
.
69.
For the compartmental system in Figure 7.39, a bolus of solute
q
1
and
is ingested into
the digestive system (compartment 3). Assume that the initial conditions are zero. Write a
single differential equation involving only variable (a)
ð
f
3
ð
t
Þ¼dð
t
ÞÞ
q
1
; (b)
q
2
. For
t
>
0, solve the system for
q
2
.
70.
Consider the three-compartment model shown in Figure 7.20 with nonzero parameters and
inputs
(c)
q
1
; (d)
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,
f
1
ð
t
Þ¼
3
u
ð
t
Þ
,
Assume that the initial conditions are zero. Write a single differential
equation involving the input and only variable (a)
and
f
2
ð
t
Þ¼
5dð
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
.
71.
Consider the three-compartment model shown in Figure 7.20 with nonzero parameters and
inputs
q
1
,
q
2
, and
K
12
¼
0
:
5,
K
10
¼
0
:
3,
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
3
ð
t
Þ¼
3d
Assume that the initial conditions are zero. Write a single differential equation involving
the input and only variable (a)
ð
t
Þ:
q
1
;(b)
q
2
;(c)
q
3
.For
t
>
0, solve the system for (d)
q
1
;(e)
q
2
;(f)
q
3
.
(g) Using SIMULINK, simulate the system from the original set of differential equations and
graph
q
1
,
q
2
,and
q
3
.
Continued
