Biomedical Engineering Reference
In-Depth Information
This chapter will guide the reader in choosing the suitable model for the fre-
quency range where respiratory input impedance needs to be analyzed.
7.2 FO Model Selection in Relation to Various Frequency
Intervals
It is important to understand the limitations of lumped FO parametric models over
various frequency intervals. There exists no generally valid model, since the vari-
ations of the impedance values with frequency are significant, as we will see later
in this chapter. To begin with, we discuss the available FO models in order of com-
plexity.
The first model, from here-on referred to as FO1, is defined as
1
C
r
s
β
r
Z
FO1
(s)
=
R
r
+
(7.1)
with
R
r
the resistance (kPa/(l/s)),
C
r
the capacitance (l/kPa) and 0
1. This
model was initially developed for frequencies below 5 Hz, whereas the effect of the
inductance is negligible [
57
]. Therefore, when evaluating such model in the 4-48 Hz
frequency interval, one may expect poor performance results.
The second model included in our discussion, referred to as FO2, is obtained
from (
7.1
) by adding the inductance term [
58
]:
≤
β
r
≤
1
C
r
s
β
r
Z
FO2
(s)
=
R
r
+
L
r
s
+
(7.2)
As described in Chap.
3
, experimental results show that in several patients, the real
part of the complex impedance may increase with frequency. Splitting (
7.2
) in its
real and imaginary parts yields
cos
β
r
π
2
L
r
ω
sin
π
2
sin
β
r
π
2
1
C
r
ω
β
r
1
C
r
ω
β
r
Z
r
(j ω)
=
R
r
+
+
j
·
−
(7.3)
Hence, it can be observed that when frequency increases, the real part of the term in
C
r
decreases, therefore unable to characterize correctly the impedance. However, if
the model is evaluated in a frequency range in which the real part of the impedance
is decreasing with frequency, the model performs well.
The third model (FO3) introduced in the discussion contains an extra FO term in
the inductance:
1
C
r
s
β
r
L
r
s
α
r
Z
FO3
(s)
=
R
r
+
+
(7.4)
which is in fact (
3.10
). This model is able to counteract the limitation of FO2 and
captures both increasing, as well as decreasing variations with frequency in the real
part of the impedance.
