Biomedical Engineering Reference
In-Depth Information
Fig. 5.5
Impedance by means of complex (
left
) and Bode-plot (
right
) representation, for the
R
-
L
-
C
(
continuous line
)andthe
R
-
L
-
C
-
G
(
dashed line
) model structures
which can be re-written as
L
e
1
s)
K(λ, χ)(W
d
(s))
n
1
/(R
e
1
+
Y
N
(s)
≈
(5.37)
with the fractional order
n
given by
log
(λ)
log
(λ)
n
=
(5.38)
+
log
(χ)
In our specific case we have
1
/(R
e
1
+
L
e
1
s)
Y
N
(s)
=
(5.39)
(
1
/R
e
1
C
e
1
s)
n
K(λ,χ)
·
Consequently, the impedance is given by
1
K(λ,χ)
·
(R
e
1
+
L
e
1
s)
Y
N
(s)
=
Z
N
(s)
=
(5.40)
(R
e
1
C
e
1
s)
n
The respiratory tract is simulated in a similar manner as explained in the previ-
ous section, with the same values for the upper airways and the gas compression
impedance. There is no information upon the upper airway values for
G
UA
, thus
we take arbitrary values for
G
UA
=
. The total impedance from (
5.29
)
is then calculated and depicted by means of its real-imaginary parts in Fig.
5.5
-
left, respectively, by its equivalent Bode-plot representation in Fig.
5.5
-right. Notice
that in these figures, we show the impedance in two cases: when the airway tube is
modeled by the
R
-
L
-
C
element, and by the
R
-
L
-
C
-
G
element, respectively. This
comparison allows capturing the effect of the conductance element at frequencies
below 0.1 rad/s.
A similar FO behavior can be observed as in Fig.
5.4
. This is again in accordance
to the theoretical result from relations (
5.34
) and (
5.38
), which shows that only the
ratios for
R
m
+
1
/R
m
and
C
m
+
1
/C
m
play a role in determining the value for the
fractional order at low frequencies.
1
/
[
R
UA
·
200
]
