Biomedical Engineering Reference
In-Depth Information
as possible, and the step is required to keep the eye at that location. It has been reported
that the active-state tensions are not identical to the neural controllers but are described
by low-pass filtered pulse-step waveforms. The active-state tensions,
F
ant
, are
shown in Figure 13.11 with time-varying time constants t
ac
and t
de
. It is thought that the
low-pass filtering involves the movement of Ca
รพรพ
across the cell membrane.
Some investigators have reported a different set of time constants for the agonist and
antagonist activity, and others have noted a firing frequency-dependent agonist activation
time constant. Others suggest that the agonist activation time constant is a function of
saccade magnitude. For simplicity in this chapter, activation and deactivation time constants
are assumed to be identical for both agonist and antagonist activity. The parameters are
defined as follows:
and
F
ag
F
go
is the initial agonist active-state tension before the saccade starts
F
P
is the maximum agonist active-state tension
F
gs
is the steady-state agonist active-state tension after the saccade ends
F
to
is the initial antagonist active-state tension before the saccade starts
F
ts
is the steady-state antagonist active-state tension after the saccade ends
Generally, the pulse is used to get the eyeball to the target quickly, and the step is required
to keep the eye at that location. The same innervation signal is sent to both eyes, and as a
result, they move together. We call this a conjugate eye movement.
13.5 DE
VELOPMENT OF AN OCULOMOTOR MUSCLE
MODEL
It is clear that an accurate model of muscle is essential for the development of a model of
the horizontal fast eye movement system that is driven by a pair of muscles (lateral and
medial rectus muscles). In fact, the Westheimer model does not include any muscle model
and relies solely on the inertia of the eyeball, friction between the eyeball and socket, and
elasticity due to the optic nerve and other attachments as the elements of the model. In this
section, the historical development of a muscle model is discussed as it relates to the oculo-
motor system. Muscle model research involves a broad spectrum of topics, ranging from
the nano models that deal with the sarcomeres to macro models, in which collections of
cells are grouped into a lumped parameter system and described with ordinary mechanical
elements. Here the focus is on a macro, or lumped parameter model of the oculomotor
muscle based on physiological evidence from experimental testing. The model elements, as
presented, consist of an active-state tension generator (input), elastic elements, and viscous
elements. Each element is introduced separately and the muscle model is incremented in each
subsection. It should be noted that the linear muscle model presented in Sections 13.7
and 13.8 completely revises the subsections before it. The earlier subsections are presented
because of their historical significance and to appreciate the current muscle model.
13.5.1 Muscle Model Passive Elasticity
Consider the experiment of stretching an unexcited muscle and recording tension to
investigate the passive elastic properties of muscle. The data curve shown in Figure 13.12
is a typical recording of the tension observed in an eye rectus muscle. The tension required
