Biomedical Engineering Reference
In-Depth Information
Chapter 4
Modeling the Respiratory Tract by Means
of Electrical Analogy
4.1 Modeling Based on a Simplified Morphology and Structure
Since the fractal geometry is characterized by recurrent geometry, the respiratory
system is an ideal application. Lung geometry and morphology have been studied
using CT scans in 3D form [
135
]. Already since the work of Weibel, the fractal
geometry present in the lung morphology has been employed in studies on airway
aerodynamics [
163
]. The self-similarity is related to the optimality of ventilation
and asymmetry exists in the healthy lung as well. By contrast, a diseased lung
parenchyma contains significant heterogeneities and the optimality conditions are
no more fulfilled [
66
].
One of the most comprehensive and earliest overviews on the mechanical prop-
erties of lungs is given by Mead, describing the initial attempts to quantify static and
dynamic resistive, inertial and compliant properties of lungs. His review covers both
the inspiratory and the expiratory phase, at laminar and turbulent flow conditions, in
terms of a single variable: air volume. Another important study has been reported in
[
114
] for tube-entrance flow and pressure drop during inspiration in spontaneous
ventilation. While breathing at rest, the airflow remains laminar [
66
,
114
,
120
].
A decade later, Franken developed a model for oscillating flow of a viscous and
compressible fluid in a rigid tube [
41
]. It is one of the first applications of dynamic
models to the conditions of the forced oscillations technique as applied for lung
function testing. They modified the standard measurement device for pressure and
flowatthemouthofthepatientreplacingitwitha2mrigidtubeandbasedon
the tube model, the flow was estimated (thus the pneumotachograph is replaced by
this 2 m rigid tube). They included a one dimensional model of the propagating
waves and the true thermal properties of the tube wall and found that quantitative
differences between models with and without thermal variations are negligible.
Technological and computational progress allowed to perform studies of CT
scans from the 3D topology and morphology of a human (cast) lung [
135
]. Mean
gravity and branching angles up to level 9 bifurcations for the right and the left
lobe (asymmetric morphology due to heart location) were also reported, allowing
