Physiological Modeling - Introduction to Biomedical Engineering - page 881

includes a PIRB pulse with duration of T 4 - T 3 .At T 4 , the antagonist input exponentially

decays to

F ts , with a time constant t tn 3 . If no PIRB occurs in the antagonist input, the input
exponentially rises to

F ts with time constant t tn 2 .
The agonist pulse includes an interval ( T 1 ) that is constant for saccades of all sizes as

supported by physiological evidence [11, 50]. We choose to model the change in the firing
rate with an exponential function because this seems to match the data fairly well.
After complete inhibition, the antagonist neural input has a brief excitatory pulse starting

at T 3 with duration of approximately 10 ms. Enderle proposed that this burst is generated

by PIRB, a property that contributes to the postsaccade phenomena such as dynamic and
glissadic overshoot (2002). The active-state tensions are again defined as low-pass filtered
neural signals:

F ag ¼ N ag F ag
t ag

ð 13 : 52 Þ

F ant ¼ N ant F ant
t ant

ð 13 : 53 Þ

where

t ag ¼ t gac u ð t T ð Þ ut T ð Þ Þ þ t gde ut T ð Þ ð 13 : 54 Þ

1 2 2

t ant ¼ t tde u ð t Þ ut T 3 ð ð Þ Þ þ t tac ut T 3 ð ð Þ ut T 4 ð Þ Þ þ t tde ut T 4 ð Þ ð 13 : 55 Þ

The activation and deactivation time constants represent the different dynamic characteris-
tics of muscle under increasing and decreasing stimulation.

13.8.2 Parameter Estimation and System Identification
The model presented here involves a total of 25 parameters describing the oculomotor
plant, neural inputs, and active-state tensions that are estimated by system identification.
Initial estimates of the model parameters are important, since they affect the convergence
of the estimation routine. In this model, the initial estimates are derived from previously
published experimental observations, with a more detailed discussion of the parameter
estimates for human and monkey given in Zhou, Chen, and Enderle [50] and Enderle
and Zhou [18]. Oculomotor parameters are given in Table 13.1. The transfer function for
the oculomotor plant is

s þ K se
B 2

d B

y
D F ¼

2

H ð s Þ¼ ð 13 : 56 Þ

3 2

s þ P s þ P s þ P

2 1 0

where D F ¼ F ag F ant : Using the parameter values in Table 13.1, we have the transfer func-

tion for humans as

10 5

1 : 9406 ð s þ 250 Þ

H ð s Þ¼ ð 13 : 57 Þ

10 5 10 6

3

þ 596

2

þ 1 : 208

s þ

1 : 3569

s s