Biomedical Engineering Reference
In-Depth Information
x
q
x
p1
x
p4
x
4
x
1
J
p
B
2
B
2
K
se
K
se
x
p2
x
p3
B
p1
K
p1
x
3
x
5
x
2
B
1
K
lt
F
ag
F
ant
K
lt
B
1
B
p2
K
p2
FIGURE 13.41
The mechanical components of the updated oculomotor plant. The muscles are shown to be
extended from equilibrium, a position of rest, at the primary position (looking straight ahead), consistent with
physiological evidence. The average length of the rectus muscle at the primary position is approximately 40 mm
and at the equilibrium position is approximately 37 mm. y is the angle the eyeball is deviated from the primary
position, and variable
x
is the length of arc traversed. When the eye is at the primary position, both y and
x
are
equal to zero. Variables
x
4
are the displacements from equilibrium for the stiffness elements in each
muscle, and y
5
is the rotational displacement for passive orbital tissues. Values
x
1
through
x
p1
through
x
p4
are the displace-
ments from equilibrium for each of the variables
x
1
through
x
4
at the primary position. The total extension of the
muscle from equilibrium at the primary position is
x
p4
, which equals approximately
3 mm. It is assumed that the lateral and medial rectus muscles are identical, such that
x
p1
plus
x
p2
or
x
p3
plus
x
p1
equals
x
p4
and
x
p3
equals
x
p2
. The radius of the eyeball is
r
.
equal to antagonist viscosity. The antagonist muscle is similarly modeled with a suitable
change in active-state tension to
F
ant
. Each of the elements defined in the oculomotor plant
is ideal and linear.
The eyeball is modeled as a sphere with moment of inertia
, connected to a pair of
viscoelastic elements connected in series. The update of the eyeball model is based on
observations by Robinson, presented in 1981, and the following discussion. In the model
of the oculomotor plant described in Section 3.6, passive elasticity
J
p
was combined with
the passive elastic orbital tissues. In the new linear model muscle presented in this chapter,
the elastic element
K
pe
is no longer included in the muscle model. Thus, the passive orbital
tissue elasticity needs to be updated due to the elimination of
K
pe
and the observations by
Robinson. As reported by Robinson in 1981, “When the human eye, with horizontal recti
detached, is displaced and suddenly released, it returns rapidly about 61 percent of the
K
pe
