Biomedical Engineering Reference
In-Depth Information
52.
Consider the model in Figure 7.37. The time dependence of the concentration of a
radioactively labeled solute in the plasma is
mg
100 mL
after injecting a bolus of 10 g into the plasma. (a) Find the volume of the plasma compartment.
(b) Find the transfer rates
e
1:6
t
þ
e
2:8
t
c
1
ð
t
Þ¼
143
57
mg
100 mL
,
K
12
,
K
21
,and
K
13
:
(c) Suppose the input is changed to 5
u
ð
t
Þ
mg
100 mL
,
and solve for
c
1
ð
t
Þ
and
c
2
ð
t
Þ:
(d) Suppose the input is changed to 5
ð
u
ð
t
Þ
u
ð
t
2
Þ
Þ
c
2
ð
t
Þ:
53.
A unit step input is applied to the compartmental system in Figure 7.38. The transfer rates are
K
20
¼
and solve for
c
1
ð
t
Þ
and
0
:
3,
K
21
¼
1
:
0, and
K
12
¼
0
:
6
:
The initial conditions are
q
1
0
ðÞ¼
2 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
.
54.
A unit step input is applied to the compartmental system in Figure 7.38. The transfer rates are
K
20
¼
q
1
and
0
:
3,
K
21
¼
1
:
0, and
K
12
¼
0
:
6
:
The initial conditions are
q
1
0
ðÞ¼
2 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
1
and
q
2
.
f
1
(t)
K
12
Plasma
c
1
c
2
Unknown
K
21
K
10
Urine
FIGURE 7.37
Illustration for Exercise 52.
f
1
(t)
K
12
q
1
q
2
K
21
K
20
FIGURE 7.38
Illustration for Exercises 53-68.
Continued
