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
.
77.
Consider the mammillary three-compartment model shown in Figure 7.21 with nonzero
parameters and inputs
q
1
,
q
2
, and
5dð
t
Þ:
Assume that the initial conditions are zero. Write a single differential equation involving the
input and only variable (a)
K
12
¼
0
:
4,
K
30
¼
0
:
5,
K
21
¼
0
:
7,
K
23
¼
0
:
8,
K
32
¼
0
:
2, and
f
3
ð
t
Þ¼
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
.
78.
Consider the mammillary three-compartment model shown in Figure 7.21 with nonzero
parameters and inputs
q
1
,
q
2
, and
u
ð
t
Þ:
Assume that the initial conditions are zero. Write a single differential equation involving the
input and only variable (a)
K
12
¼
0
:
3,
K
20
¼
0
:
2,
K
21
¼
0
:
3,
K
23
¼
0
:
4,
K
32
¼
0
:
6, and
f
1
ð
t
Þ¼
2
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
.
79.
Consider the mammillary three-compartment model shown in Figure 7.21 with nonzero
parameters and inputs
q
1
,
q
2
, and
K
12
¼
0
:
7,
K
10
¼
0
:
3,
K
21
¼
0
:
4,
K
23
¼
0
:
5,
K
32
¼
0
:
6, and
f
2
ð
t
Þ¼dð
t
Þþ
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
.
80.
Consider the unilateral three-compartment model shown in Figure 7.22 with nonzero
parameters and inputs
q
1
,
q
2
,and
Assume
that the initial conditions are zero. Write a single differential equation involving the input and
only variable (a)
K
12
¼
0
:
1,
K
10
¼
0
:
2,
K
23
¼
4
:
0,
K
31
¼
0
:
4, and
f
3
ð
t
Þ¼
5d
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
1
,
q
3
.
81.
Consider the unilateral three-compartment model shown in Figure 7.22 with nonzero
parameters and inputs
q
2
, and
Assume
that the initial conditions are zero. Write a single differential equation involving the input and
only variable (a)
K
12
¼
0
:
3,
K
20
¼
0
:
2,
K
23
¼
2
:
0,
K
31
¼
0
:
6, and
f
2
ð
t
Þ¼
4dð
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
1
,
q
3
.
82.
Consider the unilateral three-compartment model shown in Figure 7.22 with nonzero
parameters and inputs
q
2
, and
Assume
that the initial conditions are zero. Write a single differential equation involving the input and
only variable (a)
K
12
¼
0
:
4,
K
10
¼
0
:
2,
K
23
¼
5
:
0,
K
31
¼
1
:
0, and
f
3
ð
t
Þ¼
2
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
1
,
q
3
.
83.
Consider the unilateral three-compartment model shown in Figure 7.22 with nonzero
parameters and inputs
q
2
, and
Assume that
the initial conditions are zero. Write a single differential equation involving the input and
Continued
K
12
¼
0
:
6,
K
30
¼
0
:
2,
K
23
¼
5
:
0,
K
31
¼
1
:
0, and
f
1
ð
t
Þ¼
u
ð
t
Þ:
