Biomedical Engineering Reference
In-Depth Information
are changing with the evolution of the respiratory diseases. By contrast, the structure
and morphology of the lungs influences the mechanical properties at higher frequen-
cies, given the coupling between the various respiratory compartments [
9
]. Studies
have shown that the respiratory impedance poses several resonance (minima)-anti-
resonance (maxima) frequency intervals. It is thought that the first anti-resonance
peak (around 50-150 Hz) reflects the interaction between lung tissue and air vol-
ume and changes with respiratory disease. The second peak (between 150-600 Hz)
depends on airway walls compliance and respiratory gas properties [
44
-
46
,
133
]
and has not been yet related to changes in respiratory mechanics with disease.
The work presented in this section is based on the previous chapters where it was
shown that equivalent ladder network models preserving the human lung morphol-
ogy and structure are in good qualitative agreement with general impedance values.
We employ here two parametric models for characterizing the impedance over a
long range in the frequency domain. The first model is the recurrent ladder network
model from (
5.17
) and re-visited to accommodate for the upper airway shunt and
the second model has been recently published in [
78
,
79
]. The primary objective is
to evaluate the performance of these models in a group of 31 healthy patients. The
secondary objective is to determine from the recurrent ladder network the fractional-
order value which characterizes the specific feature of the respiratory mechanics at
high frequencies.
The measurements of the signals analyzed in this section have been performed
using the device described in Chap.
3
able to assess the respiratory mechanics in
the range 7-250 Hz. On the non-parametric estimation of the respiratory impedance
using (
3.8
), we fit the recurrent ladder network described in Chap.
5
.
For comparison purposes, we employ the parametric model given in [
78
]is
Z
m
Z
g
Z
ts
+
Z
m
Z
aw
Z
g
+
Z
m
Z
aw
Z
ts
Z
PA R
=
R
p
+
(7.15)
Z
g
Z
m
+
Z
ts
Z
m
+
Z
g
Z
ts
+
Z
aw
Z
g
+
Z
aw
Z
ts
with
R
p
the peripheral resistance,
Z
m
the impedance of the upper airway compli-
ance
C
m
;
Z
aw
the impedance of the series connection of airway resistance
R
aw
and
inertance
L
aw
;
Z
g
the impedance of the alveolar gas compliance
C
g
and
Z
ts
the
impedance of the series connection of lung tissue and chest wall resistance
R
ts
, iner-
tance
L
ts
and compliance
C
ts
. This model has been shown to be in good agreement
with frequency response values in the 4-500 Hz interval [
78
]. To our knowledge,
this is the most complete model developed for analysis of the respiratory mechanics
in the high frequency range.
The first segment in the respiratory tract is denoted by the upper airways, com-
prising the oral cavity, larynx, and pharynx. The corresponding electrical elements
are then denoted by a resistance
R
UA
, an inductance
L
UA
and a capacitance
C
UA
(see Fig.
7.31
). Since we make use of recurrent properties as given by (
5.4
), the ini-
tial values of the recurrent ladder network,
R
UA
,
L
UA
,
C
UA
, are not known and they
need to be included in the identification as unknown parameters. Next, using the
recurrent ratios from (
5.4
) combined with the geometrical ratios from (
5.1
)-(
5.3
),
the impedances
Zl
m
and
Zt
m
can be calculated.
We refer to the identified impedance
Z
REC
as the inverse of the admittance from
(
5.17
). Similarly, we refer to the identified impedance from
7.15
as
Z
PA R
.
