Biomedical Engineering Reference
In-Depth Information
Fig. 7.40
Identified
Z
REC
impedance (
circles
) fitted to
the test-case impedance data
(
stars
)
7.4.3 Relation to Physiology and Pathology
The measured impedance values in healthy subjects and the corresponding reso-
nance/anti-resonance peak values are qualitatively and quantitatively comparable to
those reported in [
39
,
78
,
79
]. Both impedance models evaluated here were able to
capture the frequency-dependence of the respiratory mechanics at high frequencies.
The idea of multiple parallel tubes to model the respiratory tree at high frequen-
cies from [
39
] is here re-visited by means of a recurrent ladder network
Z
REC
.
The ladder network model
Z
REC
captures well the variations with frequency in the
impedance in all investigated patients and the identified model parameter values are
within reasonable values from clinical insight [
112
]. One should keep in mind that
the estimated ladder network coefficients are based on recurrent relations and the
fact that this recurrence leads to the constant-phase behavior in the impedance data
is an intrinsic property of such models [
31
,
56
-
58
]. Even if these ladder network
elements are then replaced by fractional-order elements, the convergence remains
valid [
118
]. These findings support the theoretical insights on prior ladder network
developments and are in line with morphometry of the respiratory system [
31
,
39
].
The upper airway resistance values
R
ua
are similar to those identified in [
79
]. The
identified upper airway compliance
C
ua
values are slightly lower for the
Z
REC
than
the values reported in [
79
].
The identified model parameters of
Z
PA R
are close to those reported in [
39
]for
the model with bronchial elasticity and similar to those reported in [
79
].
The values for the fractional order calculated from the identified recurrent ratios
(
n
=
0
.
78) are very close to previously reported values in [
71
] for healthy sub-
jects by means of a lumped FO parameter model (average value
n
=
0
.
79). It is
remarkable that a very close FO value (average value
n
=
0
.
8) has been obtained in
[
11
] when respiratory impedance has been evaluated at low frequencies in lambs.
This suggests once again experimentally what has been theoretically shown in
[
70
,
76
,
118
], i.e. that the recurrent ladder network converges to a lumped fractional-
order model, whose fractional order is independent of frequency [
105
].
Since in [
154
,
155
] it was illustrated that the respiratory impedance at high fre-
quency is subject to bias originating from the nose clip, we re-identified the recurrent
