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Chapter 4 – State of the art of methods and instruments for analysis of respiratory parameters
4.1 Linear model of first order
The simplest lumped-parameter model proposed in literature for the identification of
respiratory mechanics in mechanically ventilated is the linear model with a series of two
parameters: a resistance R and an elastance E. This model has had great success in clinical
practice for the substance of its simplicity, the immediate interpretation of his physiological
parameters and its sensitivity to changes in lung mechanics. The output of the model at each
instant of time is:
P ( t)
= R ⋅Q(
t)
+ E ⋅ ∆V
( t)
+ P
0
where P(t) represents, as appropriate, the pressure at the mouth or the transpulmonary
pressure; Q(t) is the total flow at the mouth; ∆V(t), obtained by numerical integration of Q(t),
reflects changes in the volume of air compared with an initial reference volume; P 0 is the
pressure corresponding to Q(t) and ∆V(t) both zero. In discrete time, the parameters of
equation can easily be estimated from sample points by simple linear regression. Recent
studies [Avanzolini G. et al, 1995; Bates J.H.T. and Lauzon A.M., 1992] have shown that this
model provides a too simplified representation of the non-linearity and multi-compartmental
aspects of respiratory mechanics. It is for example known as upper airway resistance is a
nonlinear function of flow and as the total resistance depends on the tidal volume and is
different during inspiratory and expiratory, being a continuous function of time throughout
the respiratory cycle. Therefore, the parameter estimates based on first-order model depends
not only on the state of the patient, but also by the experimental conditions (ventilation
characteristics) as the model assumes a linearization in the neighborhood of set point.
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