Biomedical Engineering Reference
In-Depth Information
Fig. 3.2
Structure of the viscoelastic model from [
111
].
R
aw
airway resistance;
C
s
static compli-
ance;
R
ve
viscoelastic tissue resistance;
C
ve
viscoelastic tissue compliance
3.3 Lumped Models of the Respiratory Impedance
3.3.1 Selected Parametric Models from Literature
With the real (Re) and imaginary (Im) parts of the complex impedance from (
3.8
)at
hand, parametric identification can be further employed to characterize the respira-
tory impedance. Unlike non-parametric modeling, parameterization has the advan-
tage of providing concise values for the variables of interest. With the frequency-
dependent impedance curves at hand, by means of identification algorithms [
136
],
the non-parametric data may be correlated with the models consisting of electrical
components that are analogous to the resistances, compliances, and inertances in-
herent in the respiratory system [
116
]. For this study, we selected several reported
models closely related to the physiology of human lungs. If not mentioned explicitly,
the units of model parameters are given for resistance in cmH
2
O/(l/s); for inertance
in cmH
2
O/(l/s
2
) and for compliance in l/cmH
2
O.
One of the first models reported in the literature and also the simplest is based
on analogy of the respiratory system as a tube denoting the central airways and
a balloon accounting for the inspiration and expiration changes in volume of the
lungs. This pipe-balloon analogy can be described as a RLC series electrical cir-
cuit [
32
]. In his initial attempts to characterize input impedance with a series RLC
model structure, DuBois observed that over the 1-15 Hz frequency range, the
inertance is a factor which must be negligible at ordinary breathing frequencies
(
0.0004 cmH
2
O/(l/s
2
)), but that inertia and compressibility of alveolar air become
factors of increasing importance as the test frequency is increased. He also found
rather high values for the airway resistance (3.8 cmH
2
O/(l/s)) in the 2-10 Hz fre-
quency range. He concluded that the mechano-acoustical (equivalent) system must
be more complex in order to be able to capture the true properties of chest and lungs.
This simple model is unable to represent the frequency-dependent real part of the
complex impedance (resistance) found later by other authors and therefore it has not
been included in the consequent discussions.
To characterize the respiratory mechanical properties at low frequencies, Navajas
proposed the model from Fig.
3.2
, including a linear viscoelastic component for the
tissues [
111
], with
R
aw
airway resistance;
C
s
static compliance;
R
ve
viscoelastic
≈