Biomedical Engineering Reference
In-Depth Information
The agonist time constant reported by Bahill and coworkers [4] is a function of motoneu-
ronal firing frequency; the higher the rate, the shorter the time constant. As explained, this
is because large saccadic eye movements utilize fast muscle fibers and smaller saccadic eye
movements utilize slow muscle fibers. There are two muscles involved with a horizontal
eye movement: the agonist and the antagonist muscles. The agonist muscle forcibly con-
tracts and moves the eyeball (fovea) to the target location. The antagonist muscle is
completely inhibited during the pulse phase of the trajectory. Keep in mind that muscles
are always under tension (tonic state at primary position) to avoid slack.
The control signal from the CNS to each muscle is a series of pulses or spikes due to the
action potentials of the motoneurons, as illustrated in Figure 13.10. This diagram illustrates
a typical pattern observed during a series of fast eye movements in both horizontal direc-
tions. Notice that during a movement in the “on” direction (lateral), the rate of firing
increases greatly; in the “off” direction (medial), the firing rate is zero. Also, notice that
the burst firing starts approximately 5 ms before the saccade begins and that the longer
the neurons fire, the larger the saccade. There is a large, nonconstant time delay between
the time a target moves and when the eye actually starts to move. This is due to the
CNS
system calculating the forces necessary to bring the fovea to the target location. This move-
ment is
(not guided) to the extent that there are no known stretch receptors indicat-
ing muscle activity.
ballistic
13.6 THE 1984 LINEAR RECIPROCAL INNERVATION
SACCADIC EYE MOVEMENT MODEL
Based on physiological evidence, Bahill and coworkers in 1980 presented a linear fourth-
order model of the horizontal oculomotor plant that provides an excellent match between
model predictions and horizontal eye movement data. This model eliminates the differ-
ences seen between velocity and acceleration predictions of the Westheimer and Robinson
models, and the data. For ease in this presentation, the 1984 modification of this model
by Enderle and coworkers is used. (A more thorough presentation of this model is given
in Enderle, 2010a.)
In the previous analysis,
are nonlinear functions of velocity. We can linearize
these functions by approximating the force-velocity family of curves with straight line
segments as illustrated in Figure 13.29. Antagonist activity is typically at the 5 percent level,
and agonist activity is at the 100 percent level. Thus, we can assume that
B
ag
and
B
ant
B
ag
and
B
ant
are
constants with different values, since the slopes are different in the linearization.
Using the linearized viscosity elements in our model of the eye movement system, we
write the linear differential equation that describes saccades as a function of y. The updated
model is shown in Figure 13.30. The material presented here is based on the work pub-
lished by Bahill and coworkers [4], and Enderle and coworkers [20].
To begin the analysis, we first draw the free body diagrams and write the node equations
as shown in Figure 13.31.
Þ
J
p
‥
þ
B
p
y
Node 1:
rK
se
x
ð
x
Þ
rK
se
x
ð
x
þ
K
p
y
2
1
4
3
F
ag
¼
B
ag
x
Node 2:
þ
K
se
x
ð
x
Þ
K
lt
x
2
2
1
2
þ
B
ant
x
Node 3:
K
se
x
ð
x
Þ
F
ant
þ
K
lt
x
4
3
3
3
