Biomedical Engineering Reference
In-Depth Information
Chapter 7
Frequency Domain: Parametric Model Selection
and Evaluation
7.1 Overview of Available Models for Evaluating
the Respiratory Impedance
Hitherto in this topic, we have discussed available models from literature in Chap.
3
,
and we have established an anatomical and morphological basis for the appearance
of recurrent ladder networks in Chap.
4
. The next step was to provide analogy be-
tween the respiratory airways and the electrical, respectively mechanical elements.
In Chap.
5
was also established the convergence of such ladder networks to a lumped
parametric model of fractional order, where clearly changes in the airways structure
lead to changes in the fractional-order values. Similarly, in Chap.
6
we discussed
the relation of such ladder networks to viscoelastic properties of lung parenchyma,
in a mechanical context.
Such ladder network models are useful to characterize broad ranges of frequen-
cies, since they allow (more) significant variations of model parameters with fre-
quency. However, certain variability in the fractional-order value is not captured,
making these models unsuitable for multi-fractal systems. Of course, multiple lad-
der networks will lead to multiple fractional-order lumped parametric models. It is
also meaningful to observe that the recurrent values in the airways are different for
conductive zone (i.e. nose, pharynx, larynx, trachea, bronchi, bronchioles, and ter-
minal bronchioles) than for the respiratory zone (i.e. below terminal bronchioles,
where gas exchange takes place). This already suggests that the complexity of the
respiratory system naturally requires a multi-fractal parametric model [
63
].
It has already been acknowledged in the research community that multi-fractal
lumped parametric models are indeed good candidates for characterizing the res-
piratory impedance, but the genesis of such models is not fully understood. Such
complexity in both structure and function has gathered the attention of many biol-
ogists, physiologists, anesthesiologists, and engineers [
63
]. As the emerging tools
from fractional calculus and chaos theory are rather new in biological applications,
we must recognize the need for a well-defined terminology and standardized analy-
sis.
