Biomedical Engineering Reference
In-Depth Information
1
11.
Given the Westheimer model described in Section 13.3 with z
¼
p
, o
n
¼
100 radians/s, and
K
¼
1, solve for the general response with a pulse-step input as described in Figure 13.11.
Examine the change in the response as the pulse magnitude is increased and the duration of
the pulse,
t
1
, is decreased while the steady-state size of the saccade remains constant.
12.
With the Westheimer model described in Section 13.3, separately estimate z and o
n
for 5
,
10
,15
, and 20
saccades using information in the main sequence diagram in Figure 13.11.
Assume that peak overshoot, y
(T
p
)
, is 1 degree greater than the saccade size. Simulate the
four saccades. Develop a relationship between z and o
n
as a function of saccade size that
matches the main sequence diagram. With these relationships, plot
T
p
and peak velocity as a
function of saccade size. Compare these results to the original Westheimer main sequence
results and those in Figure 13.11.
13.
Consider an unexcited muscle model as shown in Figure 13.27 with
32 Nm
1
,
K
lt
¼
K
se
¼
125 Nm
1
, and
3.4 Nsm
1
B
¼
(
F
¼
0 for the case of an unexcited muscle). (a) Find the
H
ð
j
oÞ¼
X
1
T
. (b) Use MATLAB to draw the Bode diagram.
14.
Consider an unexcited muscle model in Figure 13.38 with
transfer function
60.7 Nm
1
,
125 Nm
1
,
K
lt
¼
K
se
¼
2 Nsm
1
, and
0.5 Nsm
1
B
1
¼
B
2
¼
(
F
¼
0 for the case of an unexcited muscle). (a) Find the
Þ¼
X
1
T
. (b) Use MATLAB to draw the Bode diagram.
15.
Consider an unexcited muscle model as shown in Figure 13.27 with
transfer function
H
ð
j
o
32 Nm
1
,
K
lt
¼
K
se
¼
125 Nm
1
, and
3.4 Nsm
1
0 for the case of an unexcited muscle). If the muscle is
linearly stretched from 3 mm to 6 mm over a time interval of 0.003 s, that is,
B
¼
(
F
¼
x
1
(
t
)
¼
tu
(
t
)
T.
16.
Consider an unexcited muscle model in Figure 13.38 with
(
t
0.003)
u
(
t
0.003)
þ
0.003, then find the tension
60.7 Nm
1
,
125 Nm
1
,
K
lt
¼
K
se
¼
2 Nsm
1
, and
0.5 Nsm
1
(
B
1
¼
0 for the case of an unexcited muscle). If the muscle
is linearly stretched from 3 mm to 6 mm over a time interval of 0.003 s—that is,
B
2
¼
F
¼
x
1
(
t
)
¼
tu
(
t
)
T.
17.
From the horizontal eye movement model in Figure 13.30, derive Eq. (13.35).
18.
From the horizontal eye movement model in Figure 13.41, derive Eq. (13.48).
19.
From the horizontal eye movement model in Figure 13.46, derive Eq. (13.51).
20.
Using the linear homeomorphic saccadic eye movement model from Section 13.6, simulate
the following saccades using SIMULINK: (a) 5
, (b) 10
, (c) 15
, (d) 20
.
21.
Using the linear homeomorphic saccadic eye movement model from Section 13.7, simulate
the following saccades using SIMULINK: (a) 5
, (b) 10
, (c) 15
, (d) 20
.
22.
Using the linear homeomorphic saccadic eye movement model from Section 13.8, simulate
the following saccades using SIMULINK: (a) 5
, (b) 10
, (c) 15
, (d) 20
.
23.
Consider the linear homeomorphic saccadic eye movement model given in Eq. (13.35).
(a) Find the transfer function. (b) Use MATLAB to draw the Bode diagram.
24.
Consider the linear homeomorphic saccadic eye movement model given in Eq. (13.48).
(a) Find the transfer function. (b) Use MATLAB to draw the Bode diagram.
25.
Consider the linear homeomorphic saccadic eye movement model given in Eq. (13.51).
(a) Find the transfer function. (b) Use MATLAB to draw the Bode diagram.
26.
Verify the length-tension curves in Figure 13.39.
(
t
0.003)
u
(
t
- 0.003)
þ
0.003, then find the tension
Continued
