Biomedical Engineering Reference
In-Depth Information
and a separate controller for each muscle pair. The development of the horizontal saccadic
eye movement models in this chapter are historical and are presented in increasing complex-
ity with models of muscle introduced out of sequence so their importance is fully realized.
Not every oculomotor model is discussed. A few are presented for illustrative purposes.
13.3 TH
E WESTHEIMER SACCADIC EYE MOVEMENT
MODEL
The first quantitative saccadic eye movement model was published by Westheimer in
1954. In this model, he described horizontal saccades in response to a 20
target displace-
ment. A mechanical description of the model
is given in Figure 13.7, and a system
description is given in Eq. (13.2).
‥
þ
B
y
Þ
To analyze the characteristics of this model and compare it to data, Laplace variable analy-
sis is used. Assuming zero initial conditions, the Laplace transform of Eq. (13.2) yields
y
J
þ
K
y
¼
t
ð
t
Þ
ð
13
:
2
¼
2
s
J
þ
sB
þ
K
t
ðÞ
ð
13
:
3
Þ
and as a transfer function in standard form
o
2
n
K
y
t
¼
1
H
ðÞ¼
J
þ
sB
þ
K
¼
ð
13
:
4
Þ
s
2
s
2
þ
2zo
n
s
þ
o
2
n
where according to Westheimer's data for a 20
saccade,
s
K
J
2
o
n
¼
¼
120 and z
¼
K
p ¼
0
:
7
:
q
r
J
B
K
FIGURE 13.7
are
rotational elements for moment of inertia, friction, and stiffness, respectively, and represent the eyeball and its
associated viscoelasticity. The torque applied to the eyeball by the lateral and medial rectus muscles is given by
t(
Westheimer's second-order model of the saccade system. The parameters
J, B,
and
K
t
), and y is the angular eye position. The radius of the eyeball is
r.
