Biomedical Engineering Reference
In-Depth Information
Equation (13.32) or Eqs. (13.33) and (13.34), depending on whether the muscle is contract-
ing or lengthening, can be substituted for parameter
in the preceding equation to give
B
a nonlinear model of oculomotor muscle.
13.5.6 Passive Tissues of the Eyeball
At this point, we return to modeling the eyeball. As previously discussed, Robinson
not only described the passive properties of muscle, but he also determined the elasticity,
viscosity, and inertia of the eyeball from his experiments during strabismus surgery. With
the two horizontal muscles, Figure 13.28 describes the passive tissues of the eyeball. Note
that the passive elasticity of the eyeball,
, is a combination of the effects due to the four
other muscles, the optic nerve, and so on. The viscous element of the eyeball,
K
p
B
p
, is due
to the friction of the eyeball within the eye socket.
13.5.7 Activation and Deactivation Time Constants
The control signal that the central nervous system sends to the oculomotor system
during a saccade is a pulse-step signal as described in Figure 13.11. The signal the oculo-
motor system actually experiences is a low-pass filtered version of this signal. If we let
C(s)
¼
control signal,
F(s)
¼
active-state tension, and
H(s)
¼
low-pass filter, then
F
ðÞ¼
C
ðÞ
H
ðÞ¼
C
ðÞ
s
ð
t
þ
1
Þ
where t is the low-pass filter time constant.
x
1
θ
J
p
K
se
K
se
x
3
x
2
B
ag
K
lt
B
p
K
p
F
ant
K
lt
B
ant
F
ag
FIGURE 13.28
This model describes the two rectus muscles (agonist (ag) and antagonist (ant)), connected to
the eyeball. y represents the angle that the eyeball is rotated, and
x
1
represents the length of arc rotated.
