Biomedical Engineering Reference
In-Depth Information
input and only variable (a)
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
.
92.
Consider the three-compartment model shown in Figure 7.20 with nonzero parameters and
inputs
q
1
,
q
2
, and
K
12
¼
0.4,
K
10
¼
0.5,
K
21
¼
0.6,
K
31
¼
0.9,
K
21
¼
0.4,
K
32
¼
0.7,
K
23
¼
0.2,
K
13
¼
0.8,
e
t
u
and
). Assume that the initial conditions are zero. Write a single differential
equation involving the input and only variable (a)
f
2
(
t
)
¼
3
(
t
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
.
93.
Consider the three-compartment model shown in Figure 7.20 with nonzero parameters and
inputs
q
1
,
q
2
, and
K
12
¼
0.4,
K
10
¼
0.5,
K
21
¼
0.6,
K
31
¼
0.9,
K
21
¼
0.4,
K
32
¼
0.7,
K
23
¼
0.2,
K
13
¼
0.8, and
e
(
t
-1)
f
2
(
-1). Assume that the initial conditions are zero. Write a single differential
equation involving the input and only variable (a)
t
)
¼
3
u
(
t
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
.
94.
Consider the following three-compartment model in Figure 7.40. A 5 g radioactively
labeled bolus is injected into compartment 2. The time dependence of solute concentration
in compartment 2 is
q
1
,
q
2
, and
mg
100 mL
(a) What is the volume of compartment 2? (b) Determine the transfer rates
e
3:1069
t
þ
e
0:1931
t
c
2
ð
t
Þ¼
6
:
6271
106
:
6271
K
32
.
95.
Given a mammillary four-compartment model as described in Figure 7.26, with nonzero
parameters and inputs
K
21
,
K
23
, and
K
12
¼
0.3,
K
10
¼
0.2,
K
21
¼
0.4,
K
31
¼
0.8,
K
13
¼
0.7,
K
14
¼
0.2,
K
41
¼
0.5,
and
), assume that the initial conditions are zero. Write a single differential equation
involving the input and only variable (a)
f
2
(
t
)
¼
5d(
t
q
1
;(b)
q
2
;(c)
q
3
;(d)
q
4
.For
t
>
0, solve the system for
q
4
. (i) Using SIMULINK, simulate the system from the original set of
differential equations and graph the quantity in each compartment.
96.
Given a mammillary four-compartment model as described in Figure 7.26, with nonzero
parameters and inputs
(e)
q
1
;(f)
q
2
;(g)
q
3
;(h)
K
12
¼
0.5,
K
10
¼
0.1,
K
21
¼
0.3,
K
20
¼
0.3,
K
31
¼
0.2,
K
13
¼
0.5,
K
14
¼
0.7,
K
41
¼
0.2, and
f
1
(
t
)
¼
5
u
(
t
), assume that the initial conditions are zero. Write a single differential
q
1
K
21
K
23
q
2
q
3
K
32
FIGURE 7.40
Illustration for Exercise 94.
Continued
