Biomedical Engineering Reference
In-Depth Information
Chapter 10
Conclusions
10.1 Main Results
In this topic, the airway tree geometry and morphology was addressed to find the
origins of the fractional order appearance in impedance models of the respiratory
system. These models pose the characteristic of having a constant phase over a
frequency interval, suggesting a frequency independent mechanical efficiency of
the lungs (i.e. constant-phase models). After a careful investigation on the existing
models from literature for the input impedance, we conclude that the fractional order
models may outperform integer-order models in certain frequency intervals. Hence,
the natural question arises:
why?
The work in this topic is based on two characteristics of the respiratory sys-
tem:
1. the geometrical structure, using the intrinsic recurrence of the respiratory tree
and
2. the tissue structure, using the viscoelastic properties of lung parenchyma.
A mathematical model has been developed using the Navier-Stokes equations
and Womersley theory, leading to a relation between the air pressure and air-
flow in the airways, with respect to lung geometry, morphology and airway wall
(visco)elasticity. Further on, following the two characteristics of the respiratory sys-
tem, two analogues have been derived from this mathematical model:
1. an electrical analogue, based on the recurrent geometrical structure of the lung,
and
2. a mechanical analogue, based on tissue viscoelasticity.
Next, it was shown that the electrical analogue leads to an equivalent structure
of the respiratory tree, namely a ladder network. If approached with classic integer-
order modeling, it results in a very high-order impedance model. However, a con-
