Biomedical Engineering Reference
In-Depth Information
Fig. 3.6 Structure of the 'RLCES' proposed model [ 69 ]. R c the central resistance, L r the total
inertance, R p the peripheral resistance, C b the bronchial tube compliance, and C e the extrathoracic
compliance
studies upon the frequency dependence of respiratory resistance at low frequencies.
The added peripheral resistance R p allows for the frequency dependence observed
of the typical real impedance data, which is beyond the RLC series model's capabil-
ity. The physical justification for adding this additional component is that it models
the resistance presented by the respiratory system's small airways.
Finally, another lumped parametric model proposed recently in the literature is
based on the observations from [ 29 ] on the influence of the upper airway shunt: RL-
CES ( RLC E xtended with S hunt). In Mead's model, the influence of upper airway
shunt is taken into account by the extrathoracic compliance C e . The proposed model
is then an extension from the Extended RLC proposed in [ 29 ] combined with the
extrathoracic compliance from Mead [ 102 ]. The corresponding electrical scheme
of the RLCES model is given in Fig. 3.6 . This model is a simplification of Mead
model, with similar variables: R c , the central resistance, L r , the total inertance, R p ,
the peripheral resistance, C b , the bronchial tube compliance, and C e , the extratho-
racic compliance [ 69 ].
Hitherto, integer-order parametric models for characterizing the respiratory input
impedance have been broadly developed and tested in various lung pathologies.
Although they succeed to characterize in a clinically useful manner the mechanical
properties of the lungs, there is a major drawback: accuracy increases with the model
order and so does numerical complexity. The impedance varies significantly with
frequency, requiring high order dynamical models. This problem has been tackled
by introducing the concept of fractional calculus from mathematics, leading to FO
models.
Some of the proposed FO models in the literature are
P(s)
Q(s) =
1
C r s β r
=
R r +
+
Z r (s)
L r s
(3.9)
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