Signals and systems - Biomedical Engineering Desk Reference - page 67

of determining a system's response to such stimuli is
greatly reduced.

2.3.3.1 Analysis of linear systems

A linear system is usually viewed as acting on a specific
input signal to produce an output as shown in Figure 2.3-1 .
This is a very general concept: inputs can take many
different energy forms (chemical, electrical, mechani-
cal, or thermal), and outputs can be of the same or
different energy forms. There are several ways to study
a linear system. Here, two different approaches are
developed and explored: analog analysis using analog
models, and systems analysis using systems models.
There is potential confusion in this terminology. Al-
though analog analysis and systems analysis are two
different approaches, both are included as tools of
linear systems analysis. Hence, linear systems analysis
includes both analog and systems analysis.
The primary difference between analog and systems
analysis is the way the underlying physiological processes
are represented. In analog analysis, individual compo-
nents are represented by analogous elements. Often
these elements show detailed structures and provide
some insight into the way in which a given process is
implemented, although they may also represent pro-
cesses more globally. In systems analysis, a whole process
can be represented by a single mathematical equation.
The advantage of using analog analysis is that the model is
often closer to the underlying physiological processes.
Conversely, analyzing at the process level, as in systems
analysis, provides a more succinct description and offers
a better overall view of the system under study. In ad-
dition, the more abstract representation provided by
systems models emphasizes behavioral characteristics
and may aid in identifying behavioral similarities between
processes that contain quite different elements.

Figure 2.3-5 An early analog model of the cardiovascular
system that used electrical elements to represent mechanical
processes. In this model, voltage is equivalent to blood pressure
and current to blood flow.

what is a mechanical system is mathematically appro-
priate. In this analog model, the elements are not very
elemental, because they represent processes distributed
throughout various segments of the cardiovascular
system; however, the model can be expanded to repre-
sent the system at a more detailed level.
Figure 2.3-6 shows an analog model of the muscle
skeletal muscle that uses mechanical elements. The
muscle's force originates at the contractile element, but
this force, F o , is modified by the muscle mechanical pro-
cesses before it appears at the output, F. The internal
mechanical processes include the tissue viscosity, a sort of
internal friction, the parallel elastic element which rep-
resents the elastic properties of the sarcolemma, and the
series elastic element that reflects the elastic behavior of
muscle tendons. In real muscle, these elements are non-
linear, but are often approximated as linear providing
a linearized skeletal muscle model.
This basic model of skeletal muscle shown in
Figure 2.3-6 has been used with additional mechanical
elements to construct a mechanical model of the eye
movement

system including a pair of extraocular

2.3.3.2 Analog analysis and analog
models

In analog analysis, there is a direct relationship between
the physiological mechanism and the analog elements
used in the model, although the elements may not nec-
essarily be in the same energy modality as the physio-
logical mechanism. For example, Figure 2.3-5 shows
what appears to be an electric circuit. Of course it is an
electric circuit, but it is also an early analog model of the
cardiovascular system known as the windkessel model. In
this circuit, voltage represents blood pressure, current
represents blood flow, R P and C P are the resistance and
compliance of the systemic arterial tree, and Z o is the
characteristic impedance of the proximal aorta. Later we
will find that using an electrical network to represent

Figure 2.3-6 A mechanical analog model of skeletal muscle. The
various elements correspond to specific properties of real muscle.