Ladder Network Models as Origin of Fractional-Order Models - The Human Respiratory System - page 69

Fig. 5.15 Comparison of the RLC-ladder model performance, within the measured frequency
range, against data from healthy subjects ( left ) and equivalent polar plot representation ( right )

one has to add this extra impedance to obtain the total estimated input impedance.
By adding the values of upper airway impedance parameters: R UA =

0 . 35 kPa/(l/s),

0 . 00045 kPa/(l/s 2 ), C UA =

L UA =

0 . 85 l/kPa, one obtains satisfactory values in the
clinical range of frequencies, as depicted in Fig. 5.15 . One should keep in mind
that no study has been reported in the literature upon the variations and confidence
intervals of the upper airway parameters values. These values represent a tuning
parameter of our ladder network model, and in this particular case they have been
tuned for the averaged values of impedance given in Fig. 5.15 .
Since Fig. 5.5 shows the same result in the 25-300 rad/s frequency range for
both elastic and viscoelastic airway wall models, it is clear that the same result is
obtained for the R - L - C - G ladder network model as in Fig. 5.15 .
The impedance data collected in 10 volunteers at frequencies below 6 Hz is given
in Fig. 5.16 by means of the complex impedance values, respectively, in Fig. 5.17
by means of its equivalent Bode plot. Both figures show the statistical significance
of each measured frequency point, by means of its mean value, value distribution
within the group, and confidence intervals. These figures may suggest that the lower
the frequency, the lower the signal-to-noise ratio, due to interference with the har-
monics from the breathing frequency (about 0.25 Hz).
The values identified from the 10 volunteers tested for this study in our laboratory
are also summarized in Table 5.4 , with the identification method from Chap. 3 and
error formula from ( 3.12 ). A further comparison of this ladder network model with
two papers from literature discussing low frequency impedance values is provided
in [ 4 , 76 , 121 ].
It can be observed in the results summarized in Table 5.4 that the fifth subject
had a high initial resistance values due to inflammation of the respiratory tract (i.e.
flu). The results also show that smoking did not affect significantly the model val-
ues, suggesting that the proposed model may not be sensitive to the specific small
changes in the airways. The outlier subject indicates that age plays an important role
in determining the properties of the respiratory tree, namely an increased resistance
value, which correlates with the clinical expertise [ 53 ]. Minor differences can be