Biomedical Engineering Reference
In-Depth Information
EXAMPLE PROBLEM 13.8
Consider the oculomotor system shown in Figure 13.46 and Eq. (13.51). Given the following
initial conditions and parameter, create a SIMULINK program and plot the neural
inputs,
active-state tensions, position, velocity, and acceleration.
yð
0
s
1
, yð
0
,
0
s
2
,
yð
0
Þ¼
0
Þ¼
0
Þ¼
T
1
¼
0
:
0044 s,
T
2
¼
0
:
0259 s,
T
3
¼
0
:
0293 s,
T
4
¼
0
:
0462 s,
F
p
1
¼
1
:
06 N,
F
p
2
¼
0
:
9331 N,
F
p
3
¼
0
:
3790 N,
F
g
0
¼
0
:
4N,
F
gs
¼
0
:
5546 N,
F
t
0
¼
0
:
4N,
F
ts
¼
0
:
2895 N, t
gn
1
¼
0
:
000287 s, t
gn
2
¼
0
:
0034 s, t
gn
3
¼
0
:
0042 s,
t
gac
¼
0
:
0112 s, t
tn
1
¼
0
:
000939 s, t
tn
2
¼
0
:
0012 s, t
tn
3
¼
0
:
001 s, t
tac
¼
0
:
0093 s,
t
tde
¼
0
:
0048 s,
K
se
¼
124
:
9582 Nm,
K
lt
¼
60
:
6874 Nm,
K
¼
16
:
3597 Nm,
7223 Nms
1
,
5016 Nms
1
,
327 Nms
1
,
0022 Nms
1
,
B
1
¼
5
:
B
2
¼
0
:
B
¼
0
:
J
¼
0
:
and radius
¼
0
:
0118 m
:
Solution
We first compute the following intermediate results in MATLAB:
¼
þ
¼
b12
b1
b2
6.2239
¼
þ
¼
kst
kse
klt
185.6456
¼
¼
c3
b12*j
0.0137
¼
þ
þ
¼
c2
b12*bp
kst*j
2*b1*b2
8.1855
¼
þ
þ
þ
¼
þ
c1
b12*kp
kst*bp
2*(b2*klt
b1*kse)
1.6535e
003
¼
þ
¼
þ
c0
kst*kp
2*kse*klt
1.8204e
004
¼
¼
þ
delta
57.296/(r*c3)
3.5397e
005
p2
¼
c2/c3
¼
596.7159
p1
¼
c1/c3
¼
1.2054e
þ
005
p0
¼
c0/c3
¼
1.3271e
þ
006
The SIMULINK model is shown in Figure 13.48. The diagram in (a) is implemented using
Eq. (13.51). The input to the oculomotor plant is shown in diagram (b), with the agonist and antag-
onist active-state tensions shown in (c) and (d) based on Eqs. (13.52) and (13.53), respectively. The
agonist and antagonist neural input is shown in Figures 13.48e and f.
Figure 13.49 shows plots of position, velocity, acceleration, agonist neural input and active-
state tension, and antagonist neural input and active-state tension. From the antagonist neural
input and active-state tension plot, it is clear that the eye movement has postsaccade behavior.
Peak return velocity is -20
s
1
in Figure 13.49b, which makes it a glissade.
Continued
