Biomedical Engineering Reference
In-Depth Information
Fig. 7.31
Re-visited ladder network model to accommodate the upper airway segment
The best fit of Z REC (j ω) and Z PA R (jω) , respectively, is given by searching for
the minimum value of the cost function:
N p
( Re
x) 2
1
N p
r) 2
J =
+ ( Im
(7.16)
Ω i
where Re
x are the es-
timated real and imaginary parts, Ω i represents the set of sampling points in the
frequency domain, and N p the number of samples. The total error E T between
complex data and its estimate has been calculated as in ( 3.12 ).
=
real(Z r ) and Im
=
imag(Z r ) with Z r from ( 3.8 ),
r and
7.4.2 Evaluation on Healthy Adults
The volunteers tested for their high frequency respiratory impedance characteristic
are listed in Table 7.15 by means of their biometric values.
Figures 7.32 , 7.33 depict the calculated impedance for the 31 volunteers using
( 3.8 ) by means of its complex representation and equivalent Bode plots. The values
for the impedance are corresponding to similar measurements performed in the same
frequency interval in adults [ 39 ]. The red line denotes the averaged impedance data
from all 31 volunteers. After 70 Hz, there is increased noise amount, due to the
fixed sampling period (1 ms). However, we are measuring long data intervals (30-
40 seconds), such that the effects in the frequency response values are minimal.
Next step was to perform identification on each data set in the frequency interval
from 7-250 Hz, resulting in identified values for the ladder network in a recurrent
form Z REC . More precisely, the ladder network has resistance, inductance, and ca-
pacitance terms, in a gamma form, with ratios for each parameter as in Chap. 5 .
The number of compartments in the ladder network has been set to N =
24, ac-
cording to lung morphology [ 163 , 164 ]. The initial values for the ladder network
model were: R UA =
0 . 001 (kPa s 2 /l),
0 . 001 (kPa s/l), C UA =
0 . 001 (l/kPa), L UA =
λ
=
2 . 46, χ
=
0 . 54, α
=
1 . 15. There were statistically significant results identified
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