Biomedical Engineering Reference
In-Depth Information
In developing a muscle model for use in the oculomotor system, it is imperative that the
model accurately exhibits the static characteristics of rectus eye muscle within the normal
range of operation. Thus, any oculomotor muscle model must have length-tension charac-
teristics consisting of straight, parallel lines above 10 g tension
Since oculomotor muscles
do not operate below 10 g, it is not unimportant that the linear behavior of the model does
not match this nonlinear portion in the length-tension curves observed in the data as was
done in the development of the muscle model earlier. As demonstrated in this section, by
concentrating on the operational region of the oculomotor muscles, accurate length-tension
curves are obtained from the muscle model using just series elastic and length tension
elastic elements, even when active-state tension is zero. Thus, there is no need to include
a passive elastic element in the muscle model as previously required.
Since the rectus eye muscle is not in equilibrium at primary position (looking straight
ahead, 0
) within the oculomotor system, it is necessary to define and account for the equi-
librium position of the muscle. Equilibrium denotes the unstretched length of the muscle
when the tension is zero, with zero input. It is assumed that the active-state tension is zero
on the 45
T length-tension curve. Typically, the equilibrium position for rectus eye muscle
is found from within the slack region, where the 45
T length-tension curve intersects the
horizontal axis. Note that this intersection point was not shown in the data collected by
Collins (see Figure 13.14) but is reported to be approximately 15
.
(3 mm short of primary
position), a value that is typical of those reported in the literature.
Since the muscle does not operate in the slack region during normal eye movements,
using an equilibrium point calculated from the operational region of the muscle provides
a much more realistic estimate for the muscle. Here, the equilibrium point is defined
according to the straight-line approximation to the 45
T length-tension curve above the
slack region. The value at the intersection of the straight-line approximation with the hori-
zontal axis gives an equilibrium point of
19.3
. By use of the equilibrium point at
19.3
,
there is no need to include an additional elastic element
to account for the passive
elasticity associated with unstimulated muscle as others have done.
The tension exerted by the linear muscle model shown in Figure 13.38 is given by
K
pe
K
se
K
se
þ
K
lt
F
K
se
K
lt
K
se
þ
K
lt
x
T
¼
ð
13
:
38
Þ
1
=
¼
With the slope of the length-tension curve equal to 0
:
8g
40
:
86 N
=
m in the operating
=
¼
region of the muscle (nonslack region),
K
se
¼
2
:
5g
125 N
=
m, and Eq. (13.38) has a slope of
K
se
K
lt
K
se
þ
K
lt
ð
13
:
39
Þ
=
¼
K
lt
m.
To estimate the static active-state tension for fixation at the locations detailed in Figure 1
of Collins [7], we use the techniques by Enderle and coworkers [19] by taking Eq. (13.38) to
solve for steady-state active-state tensions for each innervation level straight-line approxi-
mation, yielding for y
is evaluated as 1
:
2g
60
:
7N
=
0
>
(N direction)
0
ð
F
¼
0
:
4
þ
0
:
0175y
N
for y
>
N direction
Þ
ð
13
:
40
Þ
