Biomedical Engineering Reference
In-Depth Information
equation involving the input and only variable (a)
q
1
;(b)
q
2
;(c)
q
3
;(d)
q
4
.For
t
>
0,solve the system
q
4
. (i) Using SIMULINK, simulate the system from the original set of
differential equations and graph the quantity in each compartment.
97.
Given a catenary four-compartment model as described in Figure 7.27, with nonzero parameters
and inputs
for (e)
q
1
;(f)
q
2
;(g)
q
3
;(h)
K
12
¼
0.3,
K
10
¼
0.1,
K
21
¼
0.5,
K
30
¼
0.4;
K
32
¼
0.6,
K
23
¼
0.4,
K
34
¼
0.2,
K
43
¼
0.7, and
f
1
(
), assume that the initial conditions are zero. Write a single differential equation
involving the input and only variable (a)
t
)
¼
10d(
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.
98.
Given a catenary four-compartment model as described in Figure 7.27, with nonzero parameters
and inputs
(e)
q
1
;(f)
q
2
;(g)
q
3
;(h)
K
12
¼
0.7,
K
10
¼
0.2,
K
21
¼
0.4,
K
32
¼
0.2,
K
23
¼
0.7,
K
34
¼
0.3,
K
43
¼
0.5, and
f
3
(
t
)
¼
20
), assume that the initial conditions are zero. Write a single differential equation involving
the input and only variable (a)
u
(
t
q
1
;(b)
q
2
;(c)
q
3
;(d)
q
4
.For
t
>
0, solve the system for (e)
q
1
;(f)
q
2
;
q
4
. (i) Using SIMULINK, simulate the system from the original set of differential
equations and graph the quantity in each compartment.
99.
Given a unilateral four-compartment model as described in Figure 7.28, with nonzero
parameters and inputs
(g)
q
3
;(h)
K
12
¼
0.4,
K
10
¼
0.1,
K
23
¼
0.6,
K
34
¼
0.7,
K
41
¼
0.4,
K
40
¼
0.2, and
f
3
(
), assume that the initial conditions are zero. Write a single differential equation
involving the input and only variable (a)
t
)
¼
20d(
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.
100.
Given a unilateral four-compartment model as described in Figure 7.28, with nonzero
parameters and inputs
(e)
q
1
; (f)
q
2
; (g)
q
3
; (h)
K
12
¼
0.4,
K
10
¼
0.1,
K
23
¼
0.6,
K
34
¼
0.7,
K
41
¼
0.4,
K
40
¼
0.2, and
f
3
(
), assume that the initial conditions are zero. Write a single differential equation
involving the input and only variable (a)
t
)
¼
20d(
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.
101.
Given a unilateral four-compartment model as described in Figure 7.28, with nonzero
parameters and inputs
(e)
q
1
; (f)
q
2
; (g)
q
3
; (h)
), 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
23
¼
0.4,
K
34
¼
0.4,
K
41
¼
0.4, and
f
3
(
t
)
¼
10d(
t
q
1
; (b)
q
2
; (c)
q
3
; (d)
q
4
. For
t
>
0, solve the system for (e)
q
1
; (f)
q
2
; (g)
q
3
;
q
4
. (i) Using SIMULINK, simulate the system from the original set of differential equations
and graph the quantity in each compartment.
102.
Given a unilateral five-compartment model as described in Figure 7.28, with nonzero
parameters and inputs
(h)
K
12
¼
0.5,
K
23
¼
0.5,
K
34
¼
0.5,
K
41
¼
0.5,
K
51
¼
0.5,
K
40
¼
0.1, and
f
2
(
), assume that the initial conditions are zero. Write a single differential equation
involving the input and only variable (a)
t
)
¼
10d(
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.
103.
Given a unilateral five-compartment model as described in Figure 7.28, with nonzero
parameters and inputs
(e)
q
1
; (f)
q
2
; (g)
q
3
; (h)
),
assume that the initial conditions are zero. Write a single differential equation involving the
input and only variable (a)
K
12
¼
0.5,
K
23
¼
0.5,
K
34
¼
0.5,
K
41
¼
0.5,
K
51
¼
0.5, and
f
1
(
)
¼
5d(
t
t
q
1
; (b)
q
2
; (c)
q
3
; (d)
q
4
. For
t
>
0, solve the system for (e)
q
1
; (f)
q
2
;
