Biomedical Engineering Reference
In-Depth Information
Fig. 4.2 The ratio between two consecutive branches belonging to consecutive levels ( left )and
between two consecutive levels ( right ) in the healthy lung for resistance R e , inertance L e ,and
compliance C e
2.09 mm 2 from trachea (level 1) to bronchiole (level 11). From level 11 onward,
these changes are not so abrupt, thus resulting in lower variance of the mechani-
cal parameters values as well. Functionally, levels up to 11 denote the conductive
zone (i.e. they transport air into and out of the lungs) and levels up to 24 denote
respiratory zone (i.e. gas exchange takes place here).
4.3 Some Further Thoughts
The set of equations given by ( 4.31 )-( 4.35 ) can be used to investigate the varia-
tions in tidal breathing pressure and flow waves caused by pathology in the nominal
function of the lung. Due to the fact that we do not seek to obtain a precise/exact
value of the pressure and flow components but merely a qualitative evaluation, a
more complex formulation may be more realistic, but may serve little to our quest
in bringing forward lumped FO parameter models. In the remainder of this chapter,
the assumptions and limitations used in the derivation of the electrical analogue are
presented.
For typical flow rates during spontaneous breathing ranging 0.5-1 l/s, wall rough-
ness is neglected since it has little effect under laminar flow conditions and for low
values of the Womersley parameter. The values of the Womersley parameter δ are
always less than 1, varying from 0.0471 in alveoli to 0.785 in the trachea. If one
compares these values of δ for the circulatory system, where values become as high
as 24, deviations from Poiseuille parabolic flow profile occur as a result [ 120 , 139 ].
This is not the case for the laminar flow conditions during tidal breathing.
We use a set of simplifying assumptions which emerged from previous studies
[ 41 , 102 ]. The pressure at the boundaries of all parts is the same at all points of the
respective boundaries. Three of the boundaries contain gas only on one side: airway
opening, alveolar surface, and body surface. Uniform pressure is valid if the gas is in
continuity condition and there is no flow. These conditions are fulfilled for the body
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