Biomedical Engineering Reference
In-Depth Information
Fig. 5.10
The estimated
impedance within the
measured frequency range for
the symmetric (*) and the
asymmetric (o) case, against
averaged data from healthy
subjects
Fig. 5.11
Equivalent polar
plot representation of
Fig.
5.10
tract is simulated by approximating each level
m
as one cell in the ladder network,
thus
N
24. The system given by (
5.17
) has been simulated starting from initial
conditions given by the upper airway tract (mouth-trachea) as from [
121
]:
=
0
.
0008
kPa s
2
/
l
and
R
UA
=
0
.
047
(
kPa s
/
l
),
L
UA
=
(5.41)
C
UA
=
0
.
01341
(
l
/
kPa
)
Notice that these values are only averaged values and they do not represent the exact
upper airway tract impedance for each individual person. Taking into account the
effect of the upper airways is done by putting the upper airway impedance in series
to that of the recurrent tree modeled by (
5.17
), in order to obtain the total estimated
input impedance.
To validate the theoretical developments, we investigate three simulated cases:
the nominal, the pathologic and the extended case.
In the
nominal case
, the total impedance from (
5.17
) is calculated with initial
values from (
5.41
) and the ratios:
λ
=
0
.
818
,χ
=
1
.
715
,α
=
1
.
764
,
for
m
=
1
,...,
13
(5.42)
λ
=
0
.
686
,χ
=
1
.
556
,α
=
1
.
783
,
for
m
=
14
,...,
24
Notice that the convergence of (
5.17
) to the form in (
5.24
) and the term in (
5.25
)
is not guaranteed, since the condition
λ>
1 is not fulfilled. It is also interesting
