Biomedical Engineering Reference
In-Depth Information
this Voigt element reduces the order of the model from fourth to third order and simplifies
the system identification. The net torque generated by the muscles during a saccade rotates
the eyeball to a new orientation and, after the saccade is completed, compensates the
passive restraining torques generated by orbital tissues.
By summing the forces at junctions 2 and 3 (the equilibrium positions for
x
3
) and
the torques acting on the eyeball, using Laplace variable analysis about the operating point,
the linear homeomorphic model, as shown in Figure 13.46, is derived as
x
2
and
þ
K
se
F
ag
F
ant
¼
...
þ
P
2
‥
F
ag
F
ant
þ
P
1
y
d
B
2
þ
P
0
y
ð
13
:
51
Þ
where
5208
:
7
d
¼
JB
12
P
2
¼
JK
st
þ
B
B
þ
2
B
B
12
1
2
JB
12
2
K
se
þ
2
K
lt
þ
B
K
þ
K
st
B
B
B
1
2
12
P
1
¼
JB
12
¼
K
st
K
þ
2
K
lt
K
se
P
0
JB
12
Full details of the derivation are provided in Enderle and Zhou [18].
13.8.1 Neural Input
Previously, we modeled the neural input to the saccade system as a pulse-step waveform.
This input has been used in many studies because of its simplicity and ease of use [4, 17, 20].
To create a more realistic input based on physiological evidence, a pulse-slide-step input is
used as shown in Figure 13.47 (based on [26]). The slide is an exponential transition from
the pulse to the step. This model is consistent with the data published in the literature (for
example, see Figure 4 in [42], and Figure 2 in [46]). The diagram in Figure 13.47 (top) closely
approximates the data shown in Figure 13.47 (bottom) for the agonist input.
At steady state, the eye is held steady by the agonist and antagonist inputs
F
g
0
and
F
t
0
.
We typically define the time when the target moves as
0. This is a common assumption,
since many simulation studies ignore the latent period and focus on the actual movement.
The overall agonist pulse occurs in the interval 0 -
t
¼
T
2
, with a more complex behavior
than the pulse described earlier. We view the overall pulse process as the intention of the
system, which is limited by its physical capabilities. The start of the pulse occurs with an
exponential rise from the initial firing rate,
F
g
0
, to peak magnitude,
F
p
1
, with a time constant
t
gn
1
.At
T
1
, the input decays to
F
p
2
, with a time constant t
gn
2
. The slide occurs at
T
2
, with a
time constant t
gn
3
,to
F
gs
, the force necessary to hold the eye at its destination. The input
F
gs
is applied during the step portion of the input.
At
0, the antagonist neural input is completely inhibited and exponentially decays to
zero from
t
¼
T
3
, the antagonist input exponentially
increases with time constant t
tn
2
. The antagonist neural input shown in Figure 13.47 (middle)
F
t
0
with time constant t
tn
1
. At time
