Biomedical Engineering Reference
In-Depth Information
way with a time constant of about 0.02 sec, and then creeps the rest of the way with a time
constant of about 1 sec
” As suggested according to this observation, there are at least two
viscoelastic elements. Here it is proposed that these two viscoelastic elements replace the
single viscoelastic element of the previous oculomotor plant. Connected to the sphere, are
B
p
1
jj
K
p
1
connected in series to
.
B
p
2
jj
K
p
2
. As reported by Robinson, total orbital elasticity is
10
7
g/
(scaled for this model). Thus, with the time constants previously
described, the orbital viscoelastic elements are evaluated as
equal to 12.8
10
6
g/
,
K
p
1
¼
1.28
10
6
gs/
. For modeling
purposes, y
5
is the variable associated with the change from equilibrium for these two pairs
of viscoelastic elements. Both y and y
5
are removed from the analysis for simplicity using
the substitution y
10
6
g/
,
10
8
gs/
, and
K
p
2
¼
1.98
B
p
1
¼
2.56
B
p
2
¼
1.98
296
x
r
296
x
5
r
:
By summing the forces acting at junctions 2 and 3, and the torques acting on the eyeball
and junction 5, a set of four equations is written to describe the oculomotor plant:
¼
57
:
and y
5
¼
57
:
F
ag
¼
K
lt
x
þ
B
x
þ
K
se
x
ð
x
Þ
B
ð
x
x
Þ
2
1
2
2
1
2
2
1
B
2
ð
x
4
x
Þ
K
se
x
ð
x
Þ
F
ant
þ
K
lt
x
þ
B
x
3
3
4
3
3
1
B
2
ð
x
2
þ
x
3
x
1
x
4
Þ þ
K
se
x
2
þ
x
3
x
1
x
4
ð
Þ ¼
J
__
þ
B
3
ð
x
x
5
Þ
K
1
x
x
5
ð
Þ
K
1
x
x
5
ð
Þ
B
3
ð
x
x
5
Þ
B
4
x
5
þ
K
2
x
5
ð
13
:
46
Þ
where
57
:
296
r
57
:
296
r
57
:
296
r
57
:
296
r
57
:
296
r
J
¼
J
p
,
B
3
¼
B
p
1
,
B
4
¼
B
p
2
,
K
1
¼
K
p
1
,
K
2
¼
K
p
2
2
2
2
2
2
Using Laplace variable analysis about an operating point yields
þ
K
se
B
34
þ
B
2
K
12
þ
B
2
B
34
‥
ag
F
‥
ant
Þ
F
ag
F
ant
K
se
K
12
F
ag
F
ant
ð
F
ð
13
:
47
Þ
:
‥
:
:
‥
x
þ
C
¼
C
x
þ
C
x
þ
C
x
__
þ
C
x
4
3
2
1
0
where
B
¼
B
þ
B
2
,
B
¼
B
þ
B
4
,
K
¼
K
þ
K
2
,
K
st
¼
K
se
þ
K
lt
12
1
34
3
12
1
C
¼
JB
B
4
12
34
C
¼
B
B
B
þ
2
B
B
B
þ
JB
K
st
þ
JB
K
3
3
4
12
1
2
34
34
12
12
2
3
C
2
¼
2
B
1
B
34
K
se
þ
JK
st
K
12
þ
B
3
B
34
K
st
þ
B
3
B
12
K
12
þ
K
1
B
12
B
34
B
K
st
2
K
1
B
3
B
12
þ
2
B
2
K
lt
B
34
þ
2
B
1
K
12
B
2
C
1
¼
2
K
lt
B
34
K
se
þ
2
B
1
K
12
K
se
þ
B
3
K
st
K
2
þ
K
1
B
34
K
st
þ
K
1
B
12
K
12
K
st
K
1
B
3
2
1
K
B
12
þ
2
B
2
K
lt
K
12
K
lt
K
se
K
12
þ
K
1
K
st
K
2
Converting from
C
0
¼
2
x
to y gives
þ
K
se
B
34
þ
B
2
K
12
þ
B
2
B
34
‥
‥
Þ
F
ag
F
ant
d
K
se
K
12
F
ag
F
ant
ð
F
ag
F
ant
ð
13
:
48
Þ
:
‥
:
3
:
‥
2
‥
1
y
¼
þ
P
þ
P
þ
P
þ
P
0
y
