Biomedical Engineering Reference
In-Depth Information
ladder network model
Z
REC
in the 5-50 Hz frequency range. The two identified data
sets are illustrated in Fig.
7.38
and there were no statistically significant differences
between them (
p<
0
.
7). We conclude that the fractional-order index is independent
of frequency, hence it is a reliable parameter to quantify the fractal properties of the
human respiratory system. There can also be speculated that age does not seem to
introduce difference in the results—as observed from the two introduced outliers pA
and pB from Table
7.16
. However, further studies will have to confirm this claim in
detail.
Intuitively, we expect that changes in resistance and compliance values of the
airways and respiratory tissue will affect the recurrent ratios. This has been shown
in previous section by a simple yet efficient example on the “test-case” impedance,
resulting in a different identified value for the FO parameter
n
. Consequently, we
expect that the value of the fractional order will be sensitive to changes originated
from different respiratory pathologies. This is also supported by our prior study on
the impulse response of fractional-order models identified from healthy and patho-
logic data, which gave different pressure-volume dynamics [
75
] and other works
[
55
]. There is also evidence in the literature showing that morphometric changes
occur in the airways with pathology and thus we have reasons to believe that our
claim is well justified [
51
,
84
,
156
].
There are several limitations present in this modeling approach. A first limitation
is that the model lacks the characterization of diffusion phenomena. However, in our
model we include a gas compression compartment to account for the gas compliance
phenomena. It is also questionable whether diffusion phenomena are important at
high frequency, since it is a slow process mainly observable at low frequencies.
Perhaps the most significant limitation in this study is the fact that we assume a
symmetric tree, whereas the asymmetrical representation is more realistic [
54
,
65
].
It is significant to note that the self-similarity is related to the optimality of ven-
tilation [
66
,
91
] and that asymmetry exists in the healthy lung as well, whereas a
diseased lung contains significant heterogeneities and the optimality conditions are
not fulfilled anymore. However, even the asymmetric representation of the Horsfield
structure [
65
] has a high degree of self-similarity and, therefore, our model results
are fairly reasonable. The major errors which may occur in this study are determined
by the heterogeneity of the human lung and the inter-subject variability that can af-
fect the recurrent values. However, these values are reported in several studies and
they have offered a good basis for investigations [
91
,
97
,
163
,
164
]. Although the air-
way tree of the human lung shows considerable irregularity, there exists a systematic
reduction of airway size [
167
]. It was demonstrated that the airway tree in different
species shows a common fractal structure, in spite of some gross differences in air-
way morphology [
63
]. On the other hand, it is indeed interesting to quantify changes
in the results if the degree of asymmetry in the respiratory tree (which is scarcely
discussed in literature) is taken into account. In our opinion, the case of asymmetry
requires a separate study, since both the 'uncertainty' in the morphology of lungs
from inter-patient variability and the asymmetry resulting from disease effects (e.g.,
COPD, cancer, etc.) can be discussed. We also suspect that the asymmetry may be
self-similar over certain regions, leading thus to a multi-fractal spatial distribution.
