Biomedical Engineering Reference
In-Depth Information
where
57
:
296
P
3
¼
C
3
C
P
2
¼
C
2
C
P
1
¼
C
1
C
P
0
¼
C
0
C
d
¼
,
,
,
,
rJB
B
4
Based on an analysis of experimental data, suitable parameter estimates for the oculo-
motor plant are as follows:
12
34
4
4
4
125 Nm
1
K
SE
¼
60.7 Nm
1
K
LT
¼
2.0 Nsm
1
B
1
¼
0.5 Nsm
1
B
2
¼
10
3
Ns
2
m
1
J
¼
2.2
0.538 Nsm
1
B
3
¼
41.54 Nsm
1
B
4
¼
26.9 Nm
1
K
1
¼
41.54 Nm
1
K
2
¼
Based on the updated model of muscle and length tension data presented in the previous
section, steady-state active-state tensions are determined as
0
0
:
4
þ
0
:
0175y N for y
ð
13
:
49
Þ
F
¼
0
0
:
4
þ
0
:
0125y N for y
<
The agonist and antagonist active-state tensions follow from Figure 13.11, which assume
no latent period, and are given by the following low-pass filtered waveforms:
F
ag
¼
N
ag
F
ag
t
ag
F
ant
¼
N
ant
F
ant
t
ant
and
ð
13
:
50
Þ
where
N
ag
and
N
ant
are the neural control inputs (pulse-step waveforms), and
t
ag
¼
t
ac
ð
u
ð
t
Þ
u
ð
t
t
ÞÞ þ
t
de
u
ð
t
t
Þ
1
1
t
ant
¼
t
de
ð
u
ð
t
Þ
u
ð
t
t
ÞÞ þ
t
ac
u
ð
t
t
Þ
1
1
are the time-varying time constants.
Saccadic eye movements simulated with this model have characteristics that are in good
agreement with the data, including position, velocity and acceleration, and the main
sequence diagrams. As before, the relationship between agonist pulse magnitude and pulse
duration is tightly coupled.
EXAMPLE PROBLEM 13.7
Using the oculomotor plant model described with Eq. (13.48), parameters given in this section,
and the steady-state input from Eq. (13.49), simulate a 10
saccade. Plot agonist and antagonist
active-state tension, position, velocity, and acceleration versus time. Compare the simulation with
the main sequence diagram in Figure 13.6.
Continued
